Are you sure that the 24V/1A are there “no question asked”?
(the device may do some controls. like resistance check before providing the 24 V out)
In theory it should work, but you never know.
You can try using an injector/splitter and a male-male jack cable to power the Ax3 taking the power from your converter, like:
http://forum.mikrotik.com/t/mikrotik-rbgpoe-usable-as-poe-splitter/152794/1