I wouldn't think so. That's the whole point of a GTY rate. To offload cabins no one is willing to pay for to people who are willing to gamble a bit and end up with a little but less than desirable cabin. But it never hurts to ask.
This happened to us and I was initially actually quite bent out of shape about it because of the tub situation. But fellow disers assured me that I would LOVE the cabin, and that the extra space is amazing! And it was! I would request one if I could (but never would, seeing as we are not disabled.) My kids learned to handle the shower. The little one would just stand there and I would rinse her hair/body with a cup. To answer your question--I don't think you can do anything. I called in a very assertive manner but the CMs stood firm that they could not change it.
we were upgraded once to a ha room and I had the same reservations about wanting it. wasn't sure what to expect. since my reservation was not a gty I thought about saying no but I am so glad I didn't! the room was amazing. yes, it only had one bathroom, not split. no it did not have a curtain I could pull across for privacy. what it did have was an amazing veranda and the room itself was huge. it was hard to go back to a regular room on our next sailing.
go in and give it a try, you may be very surprised and pleased. hope you have an amazing cruise.