What happens to this mod's compat then?

Nicer skies has no control whatsoever over the shader code being loaded and what it does. If complementary will provide an option to show the vanilla sky, then probably yes, else no. That's fully up to them, and if you want to know you can ask them. I would recommend asking in a discord server or such, as the issue tracker is usually used to report issues. (I don't mind though :) )

Probably nothing, possibly the nebulas will stop being visible with the shaders turnd on.

Would it be possible to turn the cr skies off if nicer skies is installed?