Yes it is unlocked or you wouldn't be able to use it with another carrier's SIM card.
SMS/MMS are exchanged via a carrier's cellular network only - wi-fi has nothing whatsoever to do with exchanging text messages - SMS/MMS. MMS with an iPhone requires cellular data.
I guess my reading comprehension is different from yours.
Talk, Text and Web are supported features with our service when using an iPhone. MMS is NOT a guaranteed feature when using an iPhone with Airvoice. If you would like to use this feature, the device will need to be fully UNLOCKED. Airvoice still does not guarantee that MMS will work with an iPhone even if the device is unlocked."
The carrier you are using does not guarantee being able to exchange MMS with an iPhone.
Since the iPhone was sold as carrier locked with ATT, it was "fully" unlocked by ATT and Apple or you wouldn't be able to use it with this non-supported carrier.