Would Eisenhower's health let him run in 1956?
It is possible that Eisenhower's time as President exacerbated his health issues, and that in an ATL where he was not President his health would have held up to 1956. Not certain, but possible. Being President can be very stressful.
Some people are missing the fact that Eisenhower stated privately he would endorse Truman if his opponent was Taft.
If Eisenhower is insanely popular enough to beat virtually any political opponent, shouldn't his endorsement be a substantial boost for the unpopular Truman?
Yes, I think it could have helped substantially.