I'd say the party would likely keep their titles and what not during the war, but unless their kingdom wins the war and gains an unconditional surrender, they are screwed when the war is over. If the players country wins, they will likely be sacrificed as a good faith gesture to help make the peace treaty go over more smoothly. If the player's country loses, you can bet they'll be part of the surrender agreement.
The thing about war crimes is people are rarely charged with them until after the war.