No, they don't. They'd get really viciously badmouthed at home, so no one would dare to surrender.
///Edit: Oh wait, silly me. Just described this in another thread and now denying it. Well, there is one other method to get them to surrender, and that is to take all their colonies (or maybe just the capital? don't know). That will hand all their remaining ships over to you, so if you feel really bold you could just ignore all their ships and rush forward with some highly armored crafts to take them all by storm. A maximum gain victory.
However there is no check that considers whether they are outgunned or not. That would be quite an advanced mechanic, which I have not seen anywhere in a game that doesn't treat battles in separate encounter arenas.