In Hardcore Team Deathmatch, when you die, you have to wait some time before re-spawing. While waiting, you are spectating another player on your team.
Can they hear you? Is it useless to try to warn them about danger?
I'm not 100% sure about the in-game chat, because I infrequently use it. However, I'm sure that you can use secondary chat channels (ie, Xbox Live Party Chat) while you are playing Hardcore Team Deathmatch, and that you can talk on them even while you are waiting to respawn.
This is different from Modern Warfare 2, where your chat options were limited. A spokesperson for Infinity Ward said:
I would test the in-game chat channel, but I'm going to go ahead and say that it's highly likely that it works regardless of your current state.
If you're playing on PC, and you want to communicate always, you might look into Ventrilo or TeamSpeak, both are options that the game itself has little control over and the both integrate well with FPS games.