As thatguy said, CDMA phones don't work on GSM networks, and TMobile is a GSM network. It's a different technology - to one technology, signals from the other technology sound like noise. All MetroPCS CDMA phones become useless after Metro shuts their CDMA network down. They may offer you a great deal on the equivalent TMobile phone (the TMobile version of the S3), but reflashing the phone to work on a different CDMA network is one of those "don't try this at home" things.
It's not a matter of radios, it's a matter of technology - a CDMA phone can't hear TDMA (which GSM is) signals, because it works by code, not by timeslots. IF you could make the 2G connection, then the 3G/4G/LTE connection might work (those are the "same radios") - but since the 2G connections use different technologies, it's not going to happen.
If TMobile is so sure it will work, ask them to put one of their SIMs in your phone and show you it working. (Any phone that will work on TMobile's network will work with any TMobile SIM of the same size. If they tell you otherwise, they don't know what they're talking about. That's one of the main selling points of GSM - put your SIM in any phone and it'll work if the phone isn't locked.)