I can drag and drop a page variant to move it outside of the "Variants" node - I can't use the "move page" action, though, as it has been properly disabled.

I didn't get any exceptions or errors, but such a page would obviously be very shaky to use.

You should not be able to move a page variant outside of the "Variants" node using drag and drop. It should be allowed to re-order pages inside the "Variants" node, but that's actually secondary: I'd rather not be able to move a page variant at all than move it to the wrong places.