Yes. this is a great idea and I bet its not even too hard to implement as long as TP, guesting and character names are all cross-server. I would make this cross-server chat available only for each regain separately US and EU.
Many times you are in a zone with no chatty players at all. It makes the game to feel like a single player. A cross-server chat will make this chat more vivid due to the larger number of players