Yes it can. UniFi PoE is indeed a proprietary system (hence "passive PoE"), but ToughSwitch to UniFi AP works. Sometimes you have to be careful with the voltages, there are access points (e.g. the Outdoor series) that accept 24-48V, in which case a 48V power supply is included that you must not combine with the indoor AP! However, all indoor and outdoor APs should run with the TouchSwitch.

I have been using the following in my home since September 2015:
Ubiquiti EdgeRouter X
Ubiquiti UniFi AP-3, set of 3, n300
Ubiquiti Toughswitch, TS-5-POE, 24V passive PoE
Runs with x-Sonos boxes and NAS and stream to Samsung TV, as well as mobile phone wi-fi etc. without any problems. The APs are all connected via PoE. Only the router is a little difficult to configure, but once it's up and running, it's up and running.... :-)