US MD to consulting

I’ve been researching consulting as a way to bolster my resume and position myself for future leadership/investing roles. I’m curious how hard it would be to get an offer from MBB? I went to a large, relatively prestigious state school for all my training: undergrad, medical school (for which I was the recipient of a merit-based scholarship), and am now in residency. Some people act like MDs have a really good chance but others say it does not bolster you that much. Is an interview offer to MBB attainable? I am pretty confident that I’d do well but wondering if I’d get screened out before even getting a chance.