Stannis wasn't pro-war, and he had a hard time deciding. He eventually chose his duty towards hisfamily over his duty towards the targaryens. In the end he believed that to be the more right thing to do.
Even if Dany (and possible Jon) come a knocking, i'm pretty sure he'll see them as nothing more than new usurpers. That he considers the Targaryens lost their crown, and their rights on westeros when they lost the war. And that as the rightful king (and eldest Baratheon) it is his duty to enforce and protect the new royal lineage against all usurpers (including his kid brother)
If Robert had legitimized Edric Storm, i see him standing aside in his favor. But not for renly, Dany, Jon, ... .