The arguments over whether they were allowed to run for office would be interesting too. I've just had a look at the USA constitutional requirements for their president and it doesn't explicitly rule it out even for their highest office. It's not really covered, though I'm sure the writers would have vehemently objected to it if they weren't long dead. But when it comes to legal matters in the USA, the written word of their constitution carries a lot of weight.
As I understand it, to run for President of the U.S.A., you have to be either a natural born citizen of the U.S.A., or a citizen at the time of the adoption of the U.S. Constitution, which was 1787, so that’s going to rule out anyone less than 230 years old.
In addition, the candidate for President must be 35 years of age, and a U.S. resident for 14 years, (presumably consecutively).