[CentOS] How to export X displays

> One other question. If a program is already running on the remote machine and you want to move the display to the local machine, can that be done? 

No.

> 
> i.e. I have Thunderbird already running on the remote machine, and would like to move it to the local machine. 
> 
> Would that work? Or would it be necessary to kill the remote process and re-start it with the tunneled X session?

You can just start a new one BUT not with a tunneled X session. You have 
to first make sure the local X server is running and you point it to the 
local X server through the DISPLAY variable