The question is not really if Trump could go on the show, but whether he would be entertaining in the 'Between Two Ferns' format. The guests on the show always have to be self aware enough to be able to take a joke at their own expense. Trump simply lacks the self awareness to be funny in the way the show would want.
Trump has always shown that he is very thin skinned and narrow minded. Even before he chose to run as a presidential candidate, he demonstrated many times in his business dealings and on his own television show just how thin skinned he is. He only gets worse as he gets older.
Trump does not have a good sense of humor, at least not about himself. He is a terrible person and cannot stand the kind of abuse that he would have to put up with. He was only able to appear on Saturday Night Live when they game him complete control of the show and that was a terrible episode.
Donald Trump has shown himself to be thin-skinned on many occasions. Trump does not take criticism very well; often responding with hateful attacks against critics. He is probably too thin-skinned to appear on the Between Two Ferns show. Trump is going to need a thicker-skin if he is going to be president of the United States.