Well you would be in good company with the other hundred applicants who have the same idea if you did, as it is one of the
six personal statements in psychiatry but as mentioned above it does tend to have the potential to backfire. The way to think about info in your PS - is this something that you want all the faculty and co-residents to know? (because they will be reading your PS and interviewing you or ranking etc). So bear that in mind.
My advice for personal statements is the keep it boring. Tell us about what excites you about a career in psychiatry, what your career goals are, any relevant past experiences (e.g. volunteering, clinical experiences, research, teaching, past career), and what you are looking for in a residency program. The clarity of the writing and quality of written communication are just as, if not more, important than the content. Use lots of action words, convey lots of enthusiasm, and have a generally positive tone, even if there are some more sombre parts to your story. No one wants to read a depressing PS.
And especially for IMGs, make sure that the English good - spelling, punctuation, grammar, correct use of idioms. And don't put anything like "I am honored to apply to your esteemed residency program" which a lot of foreign grads seem to have learned from somewhere.
Also remember doctors are horrible people and will judge you for being sick. Probably best to avoid mentioning any illness (mental or physical) unless it is unavoidable. An alternative perspective, is you may not want to match at a program that would judge you so. However, as psychiatry is somewhat more competitive than in the past, I am not sure I would advise all but the most stellar applicants to carry that attitude.