GSM and CDMA don't really work that much differently. Neither has a constant-on radio, they register with a tower and then periodically check for a tower.
The main difference is one uses TDMA (GSM) and the other users CDMA for voice calls. (Time Division Multiplexing vs Carrier Division Multiplexing).
Text messaging is a side-effect of CDMA packet framing - it had to be tacked-on to GSM since it didn't utilize the same connection design.