Is Multisite Language Switcher compatible with any theme?

No there is no such a list. In theory every theme is compatible … for example: I use a Genesis-Theme, my wife has a theme from Elegant Themes installed and I know some custom themes too where this plugin is active.

It really depends on what your are looking for…

Thank you for the answer. I want to the plug in with Avada Theme. Is there any confirmation about compatibility?

No I don’t know this theme. But there should be no problem to try it.

Thank you!