Do you think the Baratheon historic closeness to the Targaryen dynasty was due to them being sort of “backup” Targaryens in case shit hit the fan?

There’s a couple problems with that description:

1. The Dance of the Dragons. Borros wasn’t exactly chummy with Rhaenrya, and his alliance with Aegon II was purely instrumental. And given that the blacks won, the Baratheons were out of royal favor for some time. 
2. The Velaryons. Closer ties to Aegon than even Orys Baratheon, three marriages into House Targaryen (Alyssa, Laena, Daenaera), and three Targ marriages into House Velaryon (Rhaenys, Rhaenrya, Baela). Plus they have the Valyrian look that the Baratheons don’t.
3. Lyonel’s Rebellion. Sort of a break in relations, I would say. But Rhaelle’s marriage into House Baratheon seems to have been the first Targ-Baratheon marriage, since Aemond never consummated his bethrothal as far as I know. 

So I wouldn’t call them backup Targs.