Only Yes for the player in a campaign/story mode.
Personally I'd prefer if death were a temporary setback ala the Sauron example. To avoid the "hunt down the remaining enemies" problem I think it should be tied to an artifact of some sort. Sort of like a mobile capital city. If it hasn't been "deployed" and your sovereign bites it, then game over. This lets you have both a "capital" site while allowing your sovereign to move about (Though there could be bonuses for keeping all of your eggs in one basket.)
If they want a inter-marriage mechanic to be a viable strategy for winning, then it has to be possible to defeat a player while some of his territory is still intact and valueable. If you were playing as the 'civ' and not as the sovereign, then there is no reason for the player to surrender until his last city is gone.
The old Koei game Genghis Khan II had an interesting mechanic that most players today would find odious if used normally, but I think it could work here. In GKII, you didn't control all of your provinces directly - you only could control one at a time. All other provinces were ruled by proxy. If your sovereign died, you could do this to reflect the loss of central authority. If not for the player, then at least the AI, perhaps. There's nothing quite like decapitating a kingdom and watching them tear themselves apart.