I'm fairly sure they wouldn't let you do a MD/PhD regardless of funding source. The contract won't even pay for a retake year if you need to repeat, let alone give you an indefinite stipend for a PhD. You sign for a 2, 3, 4 year scholarship and that's how many years you get, and immediately after those years you go active duty and pay it back.
They want a doctor, not a research scientist. That's what they hire PhDs for and they don't offer any incentives for PhD programs afaik like HPSP. There are some MD research billets but you will not spend your career in a lab with MD/DO after your name.
Frankly idk why you'd want to do HPSP with a MD/PhD. You already get full tuition and a stipend, what's the point?