Will I be able to chat while I'm on the respawn screen with the new chat widget?

I don't know that answer. Do you have a preference?

Yes. I would like to talk to people while I'm waiting to be recovered.

Well, I can say this: in general, this is part of the discussions that we've had on the UI, specifically for chat during your gameplay, that if you're downed, you should be able to chat. And so I would say that yes, if you follow that decision, then if you're on the respawn screen, you should be able to chat as well.