Yes. A friend of mine joined my game after playing AC3 and blew Josh up with a grenade (oops it's been so long, I'm used to the other controls). Now, he's greyed out whenever I play. He can still call him up whenever he wants though.
Only if they die in multiplayer do they stay dead forever, and that's because of a glitch most likely. There's a way to fix it though. If they die in single player they will eventually come back, it takes like an hour of game time though.
"It felt like the music was aimed right at me... like a missile!"
The permanently greyed out homie, is actually a glitch from using homies in multiplayer its just best to never call homies in multiplayer.
Homies you kill take about 15-30 minutes to come back just like if you dismissed them
Supposedly the way to fix it is to join someone and have them call the homie that is glitched (it won't be glitched for them unless they already had it glitched before you joined) then save and quit, then play single player and wait the 15-30 minutes cooldown for it to recharge, this can also be used to unlock the other homies from the Burt/Swat and Zombie Homie choice
Little King of LBP Level Recordings http://www.youtube.com/user/JHKthree