In the book Fire and Blood, Orys Baratheon was rumoured as half bastard brother to the Conquerors sired by Lord Aerion Targaryen. So if the rumor was true, the Baratheon have Targaryen blood from Orys who was bastard son of Lord Aerion Targaryen. And during the Dance of the Dragons, the dragonseeds claimed the dragons, just like Ulf who claimed he was bastard son by Baelon and Hugh Hammer bastard son of Saera (in tv show, in the book we still don’t know yet).
And now in the main event (game of thrones), does the Baratheon could have claimed dragon too? Because the Baratheon descendent from Orys who was bastard son of Lord Aerion Targaryen. Also do the other houses like Martell, Plumm, etc could have claimed dragon too? (As we know many Targaryen married to the other houses) or just Dany who brings back the dragon with her magic?
Theoretically, they can try and test it out....but they'd not likely risk that even Targs who are "imbued with enough dragonlord 'blood'" can be rejected by a dragon. Alyn Velaryon/of Hull tried to claim a dragon and nearly died, while his older brother successfully bonded with Seasmoke. Their father was Corlys Velaryon and their mother was presumably of Andal-descent, Marilda of Hull. The Velaryon are not and were not dragonriders/dragonlords, but I don't think the ability itself was confined by that hierarchy; we have reason to believe that the first Valerian's didn't have an sibling-marriage-oligarchy that persisted into Old Valyrian since AWoIaF says that the Valyrians were (maybe nomadic) shepherds. So there's reason to think that MOST if not ALL Valyrians and their descendants could bond with a dragon successfully IF they either convince them to bond or the dragon chooses to or it's through "cradle bonding" and whatever mysterious compulsion hatches the egg to bond. If Brown Ben Plumm could be friendly and get close to dragons as the main series let's us know, there's even more reason to at least accept the possibility.
To put it simply, there's a strong theory towards "perhaps yes", but nothing is proven-proven yet.
