Yes. Yes, Power over Ethernet (PoE) will 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 the voltage it requires, 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.
802.3af and 802.3at PoE standards have a distance limit of 100 meters or 328ft which is also the limit for the data transmission for Ethernet cables.
Figure 1: EPE-24R proprietary 24V/1A PoE injector
Figure 2: EPA5006GAT 802.3af/at PoE injector