> does the CDMA module only work if you bought the phone from a CDMA network operator
Yes. They program it with your subscriber number at purchase. Technically they could reprogram phones not sold by them with your subscriber number, but they don't (to force you to give them more money).
There does exist a CDMA version of the SIM (RUIM? something like that). China Mobile uses it, and I think au/kddi do too. American carriers do not.