Hello,
Doctors certainly do get admitted to b-school. But I believe you face some
high hurdles in getting admitted to top tier b-schools including Tuck.
Most doctors who attend b-school are seeking to leverage their career and experience to go into organizational leadership roles in some area of healthcare industry. (By the way, I don't know the percentage, but it is very small.)
AND many people successfully apply to b-school in order to
change careers. But you need something more than the idea that you’d like a profession in order to be a credible applicant. The adcom will want to see deep knowledge of your target industry (even if not direct), will want to see affirmative reasons for your career change (they won’t care that you don’t like your current career and it might even be seen as a negative factor that you followed it for so long before taking initiative to change). Finally, they’ll want to see a plan for how you would get employed in your target industry, since most finance companies want to hire people with a related background.
If you want to pursue a career in finance, perhaps try to gain experience and exposure to the industry first, then apply to b-school.