Is it possible to add extra animation tracks via inherited scene so they are kept.
You can add additional tracks to a AnimationPlayer animation, which should add those same tracks in the AnimationTree. When you have a AnimationPlayer selected, there is a little green plus button near the bottom of the screen (on the right I think) which will let you add a new track.
Will AnimationTree play function tracks?
I do not know, but I think it should. It should work with Godot 3.1 since most of the animation tree/player/stuff has been reworked.