So this is the risk of the GT rooms. Definitely money savings, but you are playing the lottery. Sometimes you win.... sometimes....
I agree with posters that noise can come from anywhere. Definitely had some noisy neighbors on cruises. But I also know there are certain rooms that are a definite NO for me (from experience) and I won't book a GT that could put me in any of those rooms. It's not worth the risk.
Here is my opinion on the two main noise issues you mentioned.
Gym noise is relegated to daytime hours. If you are already up at 6:00am everyday and go to bed at 11:00pm, you may not care overmuch about gym noise. But if thumping/pounding noise during the day when you head to your room for a break bothers you, it could be an issue.
Same for the house keeping closet. It's intermittent noise, they load the carts and heard off to clean.
Two things to give you hope of you choose to keep the room.
First, I had a cruise in a room that ended up being one of my NO rooms. It was not pleasant to deal with for me. But it did not ruin the cruise. It caused moderate amounts of inconvenience that I now tell as a story. I don't look back at the cruise as ruined at all. I still have great memories from that cruise. It did teach me what I value in a room location though. I wouldn't have known that without the experience.
Second, things that may bother you, may not bother other people, and vise versa.
I suggest using the reviews to look for complaints about things you know bother you. Only you know wha those are, and if you don't know yet, you will once you experience them and you won't know until you try stuff out.
Thats a long way around saying only you know what is important to you, and some noises that really set off other people and cause them to write a scathing review, might not bother you in the least.
If you don't want to upgrade as others have mentioned, accept the room location as a learning experience to help you know what to better do or not do next time, and enjoy the rest of the cruise. Most of your cruise probably won't be spent in your room anyway.