(SPOILER)I think they only die if it's a story-based death then. I didn't lose any heroes except Boromir at the Black Gate, and Theoden at Helm's Deep (I tried to recreate the "FORTH EORLINGAS!" final charge and got mowed down in seconds...) but Theoden popped back up, but I wonder if he would have died permanently at the Pelennor Fields. Hmm.

...I don't even know why this stuff is spoilers xD