Asking a professor if you would be able to manage the material in their graduate course given lack of background I am a graduate student in a US chemistry department and found a class (mechanical engineering) that would be somewhat helpful for my research but is out of my discipline.  I'm not familiar with a lot of the methods used and so I was considering emailing the professor to see if it would be possible.  Would this be ok to do?
I get multiple emails about this every year, so I certainly consider it normal.  It's my impression that most faculty will.
Before you do that, see if the syllabus is available to you somewhere.  That will show the professor that you did some due diligence on your own, and may even answer your questions.  Also note whether or not the class has a firm prerequisite listed - if it does that may make this more challenging.  If it does not then that suggests to me that you've got a better chance at success.
If you're still not comfortable asking, or the professor doesn't reply, you should be able to get help with this from your academic advisor.  They may be able to secure the past syllabus for you also, so if you prefer that route it might suffice.
Another suggestion is to consider asking about auditing the class - if it's outside your department and isn't necessary for your degree, maybe that would be enough to help you with your research.  A related element would be asking to take the class pass/fail, depending on your university's restrictions on such a practice.  That would allow you to take the class and, even if it's a struggle, all you need to do is pass in order to come away with what you need from it.