Looks like for the most part, the SGS3 will work except a minor few that are getting reported as iPhones. However, those people (2 cases I've read on here alone) call the CSR to get their phones reset and then it eventually works. No further complaints since then.
I'm also seeing Tmobile is releasing their SGS3 (T999) so that might be an option soon for others who aren't after the international i9300, with similar i9100 vs t989 hardware differences again.
http://www.gsmarena.com/samsung_galaxy_s_iii_t999-4804.php
Although, development for the tmobile SGS always has lacked behind the international SGS' stuff.