Looking at its source code, I’d say there’s a very good chance it’s fully compatible outside of battle.
Make sure to load SceneCustomMenu after Live Menu and Pause, so that custom tiled backgrounds won’t be hidden behind the live backdrop.
It seems to require a base plugin that I don’t readily have, though, so I can’t actually test this right now.
Inside battles, unfortunately it resets its SceneManager._callCustomMenuFromBattle flag in a way that will glitch out when the battle is used as live background. This is likely patchable on my end, so please let me know if you’d like to open custom menus during battle.
(There could still be other glitches related to not blocking the battle processing in the right place. I’d have to properly test the plugins together to figure that out.)
Alternatively, I could easily add an option to not use a live background if a Scene_Battle is encountered on the scene stack.