Do you remember the convo between Tyrion and Tywin where Tywin said something like "I have no way to prove you aren't my son?" It was right after Tywin became the Hand of the King again, and Tyrion was asking why he was replaced.
It's all speculative. Keep in mind, he didn't have a lot of love for Tyrion anyway because he believed his wife died giving birth to him.
I just think it would be really weak for both Jon Snow and Tyrion to be revealed to secretly be Targaryen.
It's would be so cliche to do that and that's one of things I liked about Song of Ice and Fire that it avoided a lot of typical fantasy cliches.