it might, the specs say:
The PD-7001G maintains the existing PoE standard (IEEE 802.3af) parameters with double the power.
if you read the specs for the 225 it says:
Power over Ethernet (PoE): 48 Vdc (nominal) 802.3af or 802.3at-compliant source - Efficient mode PoE – power save with 802.3af PoE and limited functionality
* USB port disabled
* Second Ethernet port disabled
* 2.4-GHz 802.11n radio in 1x3:1 spatial-stream mode
* 5-GHz 802.11ac radio operates without restrictions*
Unrestricted functionality with 802.3at PoE+
so although the injector isn't formally 802.3at it would provide enough power. of course the AP might do extra checking making it not work on the unrestricted functionality.
don't believe you can 100% predict this without just trying.