It depends, if the POE injector conforms to the IEEE 802.3 POE standards, then all should be fine.
Ubiqiti were notorious for early POE devices that did not conform to the POE standards and therefore did not work as expected.
Here is a basic standards conformant POE injector:
The Tenda PoE15F PoE injector delivers power and data through one Ethernet cable for easy installation and network extension. This unit's PoE port delivers power up to 100m and is compatible with IEEE802.3af/at compliant powered devices.
www.use-ip.co.uk