Update: Got my Android dev phone, and the SIM card from the prepaid T-Mobile phone works fine (note that several people below pointed out that Sprint is using CDMA, so it will NOT work with that carrier).
Caveat: the phone is set up to require a data plan for activation, which you don't get with the prepaid T-Mobile plans. Fortunately, there's a way around that. :-) (note my comment on replacing the single quotes with the proper characters).
After tweaking the database, setting up the phone to talk to my WiFi network, and plugging in the SIM from the cheap phone, everything seems to be working fine. Obviously I haven't tried everything yet, but I can browse the web, make calls, etc.