I did a program somewhat like that, but not as extreme. I was admitted early to UC Berkeley and split time my HS senior year between HS classes in the morning and UCB classes in the afternoon as a proto-freshman. The main differences, it seems, were that my program was one year, not two, and I still got to enjoy most of my HS experience. I was 16 when I started at UCB, turning 17 that spring.
On the whole, I'm glad I had the experience but I don't think I would have wanted to do it if I had to give up senior year of HS, let alone junior and senior year. I do consider those last two years of HS, as well as college, some of the best years of my life. Those years are valuable not just for the experiences you have during that time period, but also for your future ability to relate to other people.
The upside of getting units out of the way turned out to not really be relevant for me. Between my program classes and AP tests, I started my first full year at UCB with more than a year's worth of units. I expected to graduate in three (or fewer) years. I took my grad school admissions test when I was 19, scored sufficiently well for my goals, and was ready to roll. Then I thought about it and decided I really didn't want to start grad school at age 20. So I stayed in college an "extra" year and graduated in four a month after I turned 21.
Socially, I was a college non-entity at age 16. Other students weren't mean, but it's not like any of them wanted to hang out with a 16 year old. For me, it didn't matter because I still had my HS friends and social structure. I think it would be rough coming in at age 15, and I expect you would probably trend toward being friends with other TALH participants who were in the same boat.
So on this track, you would enter medical school (assuming acceptance) at age 17? That just seems like a bad idea to me. Even if you could do it academically, you would be even more socially out of place at a medical/graduate school level at that age. Bad enough you can't even go out drinking with your peers, but you're even still jailbait. But let's say you don't care about socializing because you're hardcore student guy -- I really think you would face difficulty, and maybe even discrimination when it came to finding a job. I could see that hospitals might consider your young age a strike against you when it came to employment. As a patient, I don't know that I would want a 20 year old treating me, even if he were super-smart like Doogie Howser (that's an old TV show about a genius teenager M.D. that aired more than a decade before you were born).
All in all, I say thumbs down. But if you're serious, perhaps Lamar could put you in touch with a TALH alumnus who went to medical school on the timeline you envision for yourself. That person would probably be a good resource on what your experience might be like.