No, a widget is not a monad. I think you should rather think of it as just the description of how to draw a UI - it's a GTK concept, not a Haskell concept.

Something that could be a monad is some sort of widget builder. You would be able to imperatively describe the construction of a widget. Then "running" that monadic computation would return a widget, or something along those lines. That monad would then most likely just be some sort of state/writer monad.