user11958: Can people with poor mental health not just benefit from meditation, but realize  its goals?

user5000: 
"Can people with poor mental health not just benefit from meditation,
  but realize its goals?"

Yes, if their poor mental health is not an obstacle to calming the mind.
Otherwise, the more the poor mental health is making the mind wonder, the harder to realize the goals of meditation.

user8157: Some people with a mental health history have actually benefited from meditation. 
Such benefit is known to occur on a case-by-case basis, similar to how not every person that lives as a monk benefits from monkhood. 
Many meditation centres have experience with mental health and generally require approval from a persons's psychologist or psychiatrist before permitting attendance on meditation retreats.
I have read many sincere accounts of people reducing mental health issues with meditation. 
Also, the atmosphere of genuine metta (loving-kindness) at Dhamma centres is also helpful in reducing anxiety & other self-esteem issues. 
The loving-kindness of a Buddha radiates upon all beings, neglecting none (including fake monks). 

user471: While this answer focuses on mindfulness-based medical therapies that are derived from Buddhist meditation techniques, it does not directly promote original Buddhist meditation practices, for medical therapy.
This Feb 2015 article from Huffington Post reports that:

Mindfulness research pioneer and founder of Mindfulness-Based Stress
  Reduction, Jon Kabat-Zinn, who was in the audience at Davos, stood up
  at the end of the conversation to share his thoughts on the mindful
  revolution in mental healthcare, which he noted has been well underway
  for several decades. As Kabat-Zinn explained, research and
  testimonials from patients and clinicians suggest that we can turn
  "the medication down and the meditation up."
"We’ve seen this in the clinical domain for many years. People, in
  concert with their physicians... actually going off their medications
  for pain, for anxiety, for depression, as they begin to learn the
  self-regulatory elements of mindfulness," said Kabat-Zinn. "They
  discover that the things that used to be symptomatically problematic
  for them are no longer arising at the same level."

Patients, in concert with their physicians, could seek to try two therapies derived from Buddhist mindfulness meditation techniques, namely, the Mindfulness Based Stress Reduction (MBSR) and Mindfulness Based Cognitive Therapy (MBCT). More information can be found here and here.
MBSR was founded by Dr. Jon Kabat-Zinn. You can find his books here. His book that talks about MBSR is "Full Catastrophe Living".
Another interesting book by Kabat-Zinn is "The Mind's Own Physician: A Scientific Dialogue with the Dalai Lama on the Healing Power of Meditation".
MBCT description:

Mindfulness-Based Cognitive Therapy (MBCT) is designed to help people
  who suffer repeated bouts of depression and chronic unhappiness. It
  combines the ideas of cognitive therapy with meditative practices and
  attitudes based on the cultivation of mindfulness. The heart of this
  work lies in becoming acquainted with the modes of mind that often
  characterize mood disorders while simultaneously learning to develop a
  new relationship to them. MBCT was developed by Zindel Segal, Mark
  Williams and John Teasdale, based on Jon Kabat-Zinn’s
  Mindfulness-Based Stress Reduction program.

There is a TEDx Talk video by Dr. Zindel Segal, which explains MBCT and provides research evidence.
The three founders of MBCT and Kabat-Zinn also published a book called "The Mindful Way Through Depression: Freeing Yourself from Chronic Unhappiness".
The recently held 10th Global Conference on Buddhism (17 - 18 June 2017 in Toronto, Canada) had the theme of "Neuroscience and Mental Health: Making a Mindful Connection". You can find videos from it on their Youtube channel. There were three neuroscientists who presented on Day 1, Session 3. You can find a video of that here. There were speakers from both the sangha and the academia - you can find a list here.

11958: <p>Can people with poor mental health not just benefit from meditation, but realize  its goals?</p>
 5000: <blockquote>
  <p>"Can people with poor mental health not just benefit from meditation,
  but realize its goals?"</p>
</blockquote>

<p>Yes, if their poor mental health is not an obstacle to calming the mind.</p>

<p>Otherwise, the more the poor mental health is making the mind wonder, the harder to realize the goals of meditation.</p>
 8157: <p>Some people with a mental health history have actually benefited from meditation. </p>

<p>Such benefit is known to occur on a <strong>case-by-case basis</strong>, similar to how not every person that lives as a monk benefits from monkhood. </p>

<p>Many meditation centres have experience with mental health and generally require approval from a persons's psychologist or psychiatrist before permitting attendance on meditation retreats.</p>

<p>I have read many sincere accounts of people reducing mental health issues with meditation. </p>

<p>Also, the atmosphere of genuine metta (loving-kindness) at Dhamma centres is also helpful in reducing anxiety &amp; other self-esteem issues. </p>

<p>The loving-kindness of a Buddha radiates upon all beings, neglecting none (including fake monks). </p>
 471: <p>While this answer focuses on mindfulness-based medical therapies that are derived from Buddhist meditation techniques, it does not directly promote original Buddhist meditation practices, for medical therapy.</p>

<p><a href="http://www.huffingtonpost.com/2015/01/23/neuroscience-mindfulness_n_6531544.html" rel="nofollow noreferrer">This Feb 2015 article from Huffington Post</a> reports that:</p>

<blockquote>
  <p>Mindfulness research pioneer and founder of Mindfulness-Based Stress
  Reduction, Jon Kabat-Zinn, who was in the audience at Davos, stood up
  at the end of the conversation to share his thoughts on the mindful
  revolution in mental healthcare, which he noted has been well underway
  for several decades. As Kabat-Zinn explained, research and
  testimonials from patients and clinicians suggest that we can turn
  "<strong>the medication down and the meditation up.</strong>"</p>
  
  <p>"We’ve seen this in the clinical domain for many years. <strong>People, in
  concert with their physicians... actually going off their medications
  for pain, for anxiety, for depression, as they begin to learn the
  self-regulatory elements of mindfulness</strong>," said Kabat-Zinn. "They
  discover that the things that used to be symptomatically problematic
  for them are no longer arising at the same level."</p>
</blockquote>

<p>Patients, in concert with their physicians, could seek to try two therapies derived from Buddhist mindfulness meditation techniques, namely, the <a href="https://en.wikipedia.org/wiki/Mindfulness-based_stress_reduction" rel="nofollow noreferrer">Mindfulness Based Stress Reduction (MBSR)</a> and <a href="https://en.wikipedia.org/wiki/Mindfulness-based_cognitive_therapy" rel="nofollow noreferrer">Mindfulness Based Cognitive Therapy (MBCT)</a>. More information can be found <a href="http://www.mindfulnessstudies.com/mbct-versus-mbsr/" rel="nofollow noreferrer">here</a> and <a href="https://www.umassmed.edu/cfm/mindfulness-based-programs/" rel="nofollow noreferrer">here</a>.</p>

<p>MBSR was founded by <a href="https://www.umassmed.edu/cfm/about-us/people/2-meet-our-faculty/kabat-zinn-profile/" rel="nofollow noreferrer">Dr. Jon Kabat-Zinn</a>. You can find his books <a href="https://www.amazon.com/Jon-Kabat-Zinn/e/B000AQ12GA" rel="nofollow noreferrer">here</a>. His book that talks about MBSR is "<a href="http://rads.stackoverflow.com/amzn/click/0345536932" rel="nofollow noreferrer">Full Catastrophe Living</a>".</p>

<p>Another interesting book by Kabat-Zinn is "<a href="http://rads.stackoverflow.com/amzn/click/1608829928" rel="nofollow noreferrer">The Mind's Own Physician: A Scientific Dialogue with the Dalai Lama on the Healing Power of Meditation</a>".</p>

<p><a href="http://mbct.com/" rel="nofollow noreferrer">MBCT</a> description:</p>

<blockquote>
  <p>Mindfulness-Based Cognitive Therapy (MBCT) is designed to help people
  who suffer <strong>repeated bouts of depression and chronic unhappiness</strong>. It
  combines the ideas of cognitive therapy with meditative practices and
  attitudes based on the cultivation of mindfulness. The heart of this
  work lies in becoming acquainted with the modes of mind that often
  characterize mood disorders while simultaneously learning to develop a
  new relationship to them. MBCT was developed by Zindel Segal, Mark
  Williams and John Teasdale, based on Jon Kabat-Zinn’s
  Mindfulness-Based Stress Reduction program.</p>
</blockquote>

<p>There is a <a href="https://youtu.be/1A4w3W94ygA" rel="nofollow noreferrer">TEDx Talk video</a> by <a href="http://www.psychiatry.utoronto.ca/people/dr-zindel-v-segal/" rel="nofollow noreferrer">Dr. Zindel Segal</a>, which explains MBCT and provides research evidence.</p>

<p>The three founders of MBCT and Kabat-Zinn also published a book called "<a href="http://rads.stackoverflow.com/amzn/click/1593851286" rel="nofollow noreferrer">The Mindful Way Through Depression: Freeing Yourself from Chronic Unhappiness</a>".</p>

<p>The recently held <a href="https://www.10gcb.org/" rel="nofollow noreferrer">10th Global Conference on Buddhism</a> (17 - 18 June 2017 in Toronto, Canada) had the theme of "Neuroscience and Mental Health: Making a Mindful Connection". You can find videos from it on their <a href="https://www.youtube.com/channel/UCyPKN6eYsln1wc1vldhpNcQ/videos" rel="nofollow noreferrer">Youtube channel</a>. There were three neuroscientists who presented on Day 1, Session 3. You can find a video of that <a href="https://youtu.be/msi0T8Oi8-E" rel="nofollow noreferrer">here</a>. There were speakers from both the sangha and the academia - you can find a list <a href="https://www.10gcb.org/speakers" rel="nofollow noreferrer">here</a>.</p>
