Technically the answer is yes. But here in US, we won't see it until Q4 at the earliest.
The production of new Qualcomm 3G/LTE radio that supports non-snapdragon AP is delayed due to high demand on S4 chip from many phone makers. For Qualcomm, selling S4 is higher priority than a radio chip that snapdragon competitors can use. Samsung is unhappy about this situation with qualcomm. So they are developing their own 3G/LTE chip in parallel. But it's probably not coming in time for US GSIII release. So it will have S4 chip first.