The general consensus from those who've done it is yes.
Correct.
Their system is supposed to do it automaticly as soon as they enter your IMEI in, the replacement iphone should carry the some properties as the one you're handing in.
Unlocked or locked to AT&T or whatever carrier etc....
I would make sure to tell the Apple rep that the phone is carrier unlocked and wouldnt hurt to bring in a Tmobile sim to test out cause you know people do make mistakes at times.