Eh, noble and royal bastards were common as muck back then and not too many really thought it odd if one made it to, say, the office of a Cardinal or became the Duke of Normandy (William's original nickname, with which he also often signed his letters, was "the Bastard"). You usually didn't find known bastards from the highest offices - say, as Popes or Kings, but anything else went.

They were pretty useful "spare heirs", though, and like all high-born people tended to end up as pawns in the often marriage-related power games their parents played with other potentates.

I don't have RTW, what happens then?
They start giving you successively harder missions and eventually bluntly tell your faction head to commit suicide or they'll outlaw you. By that point of game most players tell them to shove it, which duly triggers the Big Roman Civil War where all the three factions and the Senate declare war on each other.

Anyway, I've gotten the impression that for some odd reason the MTW nations become really recalcitrant to so much as speak to you once you grow big enough. Kinda unrealistic really, but it makes sense in the game's internal logic.