You mean sharing the same GdkSurface (GTK4) / GdkWindow (GTK3) in the same widget? No, you can’t.
A widget can have more than one GdkSurface/GdkWindow—though if you’re using GTK4 you should not really use GdkSurface at all, unless you’re writing a top level widget. Multiple widgets cannot share the same windowing system surface; at most, a widget can render something on its parent’s surface.