Hello,
I am also an immigrant from Russia, actually a political refugee. I have to say that my position definitely helped me during the admissions process. First of all, although I came from Russia over 10 years ago, the admissions committee overlooked the disparity between my verbal and science MCAT scores. Second, every single interviewer asked me about Russia and what the immigration process meant to me. I got to talk about myself in a personal manner, and they got a chance to know me better. Anyone who is an immigrant has a story to tell and the adcoms really like listening to someone with a story, or so I thought. For some reason, they were very impressed with the fact that I did not have an accent (I was only 11 when I came), although none of my immigrant friends do either, they seemed to think it was an accomplishment (definitely not an accomplishment). Anyway, as long as your paperwork is all legal, which I?m sure it is, I think that your position could only help you because if not for anything else, you will have something that differentiated you from most other applicants and a story to tell. Good luck in the process and PM me if you have any other questions.