IF an update is available, it should show up in Kies (connect the phone to the PC via USB and fire up the software).
However, my friend has an unlocked Galaxy S3 from ATT, using it on a Mexican carrier and guess what? Even though I KNOW there's an update available for this phone, we've never been able to update it. No OTA, no Kies, nada. Don't know if you need to have the original carrier's SIM card to update, but it shouldn't.