Do the latest firmware update of third gen Apple TV is compatible with iOS 9.3.5?

We got a Apple TV (3th gen) in each room of our building, configured with a AirPort Express and a video projector. The employees have old iPads stuck at iOS 9.3.5 or lower.

Nowadays, it's being more and more common the minor issues when mirroring the iPad screen: lags, lost of connection, sound don't playing, etc (what normally is fixed with a connection restart with AirPort and/or Apple TV or full turn off and on of iPad).

I have never updated the Apple TV firmware (due connectivity limitations) and I suppose this update will fix most of these minor issues. BUT my fear is the retrocompatibility between the Apple TV firmware with the old iOS versions.

It is 100% secure to update the Apple TV software once I still use iOS 8 and 9 with them?