I think he hated being president so probably not? Although it depends on if how much of an ego trip he'd get from being president again.

I think he got what he wanted, fame, connections and his name on shit.

Basically, like all the talentless rich assholes that don't deserve the attention they get, he wanted his name down in history as much as possible as a form of immortality and validation that he was a 'winner'.

A simple, shallow, husk of a man that embodies all of the pointless, selfish qualities that capitalism enables and celebrates.