Honestly, I think if Trump died instantaneous there would be a massive movement claiming that the current Administration was the cause of death and they would use the most recent judicial hearing regarding Seal Team 6 as evidence towards it. There would be no proof of anything because like you said it was a natural death but that would not be enough to prove anything and I believe there would still be riots
As for if the president dropped dead, the vice president would take over and there would likely be an investigation into an assassination attempt but I don’t think anything would come out of it because like mentioned it would be a natural death.