Yes. Power over ethernet (POE) will only power the unit so long as there is enough voltage to power the unit at the end of the cable run.
The maximum distance you can power a device will vary depending on the access point and its voltage required, as well as the voltage provided by the power supply, and the quality of the cable. Cat6 cable is recommended for long POE runs.
For passive POE you should use a 24V power supply. 24V passive POE will power an OM series AP up to about 50 meters or 100-150 feet.
48V 802.3af standard POE can usually go about 100 meters/300 feet.