No need to re-activate. As long as it turns on they'll accept it. I gave them my old Droid Incredible and a Samsung Continuum and still got like $30 a piece for them. Kept our existing phones as backup.
You are correct. I traded in my old Evo 3D I had in a drawer for 2 years unactivated to T-Mobile and kept my activated (but now off-the-air) Evo LTE. Glad I did too, because the Evo LTE is a great phone which I am using as a bedroom PDA, alarm clock, and music streamer. The Evo 3D had a nearly toast battery, a flaky screen, and way outdated Android.