Actually George III was very interested in Hanover and longed to visit his family's hereditary lands. He just never got the opportune moment to do so. As for the marriage itself, the Imperial Diet would play no role in recognizing or not recognizing the marriage. That was entirely up to the Emperor, first Franz I, then Josef II. So its like this: is it in Austria's best interest to have a good relationship with London or not. I think the answer is pretty obvious.