No, I don’t think that was the assumption. For one thing, when Robert was alive, Aerys II was king and it wasn’t entirely clear what the line of succession was, given Aerys’ vacillation between Rhaegar and Viserys.
I’m sure the more “pragmatic” of the rebels – Roose Bolton, the late lord Frey, etc. – would have counselled ending the Targaryen line violently, but others would have probably gone for either keeping them imprisoned but in a means befitting their station or having them take vows as septons/septas and sending them to remote septries and motherhouses respectively.
If they weren’t going to be killed, having Aegon take the black and marrying Renly or Robert’s eventual heir to Rhaenys would’ve probably been the best (non-murderous) course of action, and it’d be a nice bit of dramatic irony that the descendant of Argella Durandon would be using a descendant of Aegon the Conquerer to shore up political claims.
This muddies the water too much, and risks having a claimant for rebels to attack and restore to their “rightful position.”
-SLAL
Why not wed Rhaenys to Stannis?
And what happens if both Stannis and Robert have sons and the ex-Targaryen loyalists start scheming to put Stannis’ Targ-blooded son on the Iron Throne?
A septa’s oath is a neater solution, imo.