Pair Sony DualShock 4 v2 with Sony Android TV
Yes, it is possible to pair Dualshock 4 v2 controllers on a Sony 2015 Android TV. I have had no success when trying to pair through the TVs Dualshock 4 settings menu, but I successfully paired three controllers (simultaneously) using the Bluetooth settings menu:


If you have a PlayStation - start by unplugging your PlayStation's power cord, since I've noticed that the controllers otherwise sometimes pair with the PlayStation instead of the TV 
Press the home button on your TVs remote and go to settings.
Go to bluetooth settings.





Go to device list





Add accessory







Now press and hold the share button on your controller. While still holding the share button - press and hold the PS button on your controller. Your controller's light should, after a couple of seconds, start to flash in a pattern of two short blinks followed by a pause repeatedly. Soon your tv should identify the controller as "Unknown"





Press the "select" button on your TVs remote control (the center button of your remote) to start pairing. The TV will identify the controller as "Wireless controller"





The controllers light will turn solid white when pairing is complete.
You should now be able to control your tv using the Dualshock 4 v2 controller. 
If you want to use the controller(s) with PlayStation again, you will need to pair the controller(s) to the Playstation using an USB cable. 


While running Android Lollipop I was able to control the TV's menus, play games downloaded through Google Play Store and use the controllers in emulators.
After upgrading to Marshmallow I'm still able to control the TV, but the experience is now pretty much ruined by heavy input lag starting about 30 seconds after pairing. I still hope to find a solution for this.