I'm not sure that I'd say "physical health" in terms of, like, conditioning. He could bulk up to 320 lbs of solid muscle, be able to lift like James Harrison, run a 4.8 40, etc. - and none of it would matter if his condition requires him to be on even moderate doses of blood thinner constantly.
The problem is NFL-level contact. Ordinary football bruising that other guys could shrug off - and especially a concussion, even a relatively minor one - could become immediately life-threatening for him. Having been a caretaker for a couple of elderly folks who were on blood thinners for similar conditions, even minor bruising simply can't be taken lightly.
IF that's Garcia's situation, I really don't see how the Pats could keep him on the team.