Yes, most injectors can also act as splitters, but they have to be tested anyway, see:
https://mikrotik.com/product/RBGPOE
http://forum.mikrotik.com/t/mikrotik-rbgpoe-usable-as-poe-splitter/152794/1
But wait a minute, the ax3 is normally powered at 24V through the jack (and gives out the same 24V or a little less on the poe-out port), if you power it at 12 V there shouldn’t be any PoE output, as the minimum is 18 V.