Wow just noticed this thread. I request
Click Menu to be marked incompatible.
I have not tried Carbonite myself as I don't have an active WoW install (I have however received a few queries into compatibility though), but if Carbonite adds an interactive frame above the minimap that will prevent the menu from generating for Click Menu.
However carbonite devs and users are free to contribute a patch for Click Menu or add some form of integration.