SeaSnake
OG
No they didn't, the saying is that madness ran in Targaryen bloodlines because of incest but even in the books and lore deformities weren't common at all.
Deformities were common in Tywin's lineage tho. If I'm not mistaken Tywin's brother Gerrion Lannister was an imp and sailed to Volantis with their valyerian steel and was never seen or heard from again.
Again Tyrion was never touched by stone men and Targaryens aren't immune to greyscale. Who is able to touch dragons has no relevance. Shit Danearys had all three of her dragons kidnapped and put in the house of the undying. Was that nigga a Targaryen because he touched them ? LOLOLOLOLOL
Gerrion was not an imp