Can I send an email to the journal editorial board explaining a specific situation about the status of my paper? I submitted a paper to an Elsevier journal, and the status is "Submitted to Journal". That was a week and a half ago. I know it's not a long time, but I have an additional issue. I just need the article to be "under review" to defend my doctoral thesis. Can I send an email to the editorial board explaining this situation? Would it be wrong to do that?
Pragmatically speaking, you have nothing to lose! I don't think it's wrong, either, as your situation seems unusual. So the clear advice would be to send the email.

However, to maximize the chance that this is effective, I do think you should be clear that this is an extraordinary request. Don't expect or demand that they will be able to grant it, and be sure to thank them for taking the time to consider your email. If you are polite and to the point about what you need, I don't see how anyone could take it wrongly, but there could be some logistical, technical, or policy reason why changing the review status is not possible.