HSA + HDHP as a med student?

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Hi all, I'll be a matriculating student at Pitt SOM this fall, and I had the idea of potentially using an HSA with a HDHP throughout my years as a student at PittMed.

A high deductible health plan through UPMC has the premium around $58 bux/month with a deductible at 5k. Our student budget lays out ~$300/mo for essentially low deductible insurance. What I'm thinking is paying the ~$60/mo for a high deductible plan, and saving the other 240 into an HSA. This way, I'm still allocating money available for any health issues, and later on down the road, if I realize that I have excess funds, then I can invest some/all of my HSA funds into an index fund until some medical expense needs to be paid in the future. Besides, the excess money is still at a loan interest rate of 6.8...if I put it into an HSA and eventually go with a index fund, is it possible for the compounding of the index fund to supercede the 6.8 interest rate?

I guess why I'm asking if this idea seems sound, is because I would consider myself in reasonably good health, and while the school requires insurance, I am not sure if I'll make good use of my insurance coverage. Thus, I feel the HDHP could cover my catastrophic stuff, and whatever I don't spend, I can save for later, which incentifies healthy habits anyway.

Thoughts?

Also, when the school mentions comprehensive insurance, would that mean an HDHP is excluded, even if it covers everything but a high deductible needs to be reached? (500 deductible vs 1350, 2600,5000 deductibles)