We were on the 9/11 Magic and have a two year old DD who was within 60 days of her 3rd birthday and potty trained. We talked to the CM at registration about the possibility of her being allowed to attend the 3-4 club. The CM took our information and said she would talk with her manager and we would get a call back that afternoon with their decision. When they called back, they said that she was welcome to come that night for a 'trial' where we would stay in the Cub with her and they would observe how she handled being there, following directions, participating with other kids, etc. About 30 minutes after we were there, CM Duane talked to us and felt like she was doing fine and we could officially register her.
We always took her potty right when we would check her in and she was never there more than 1-2 hours-- the 'norm' for her was about 45 minutes. If her sister's group (5-7's) was also in the Club, she would last a little longer. We would often peek in on her just to see how she was doing. I don't think she ever had to go to the potty on her own-- though they are child size and easy to use.
We had friends on the cruise who's DD was only about 2 1/2 and not totally potty trained (needed pull-ups) and they were not granted permission to register her. I think it really is a case-by-case basis dependant upon several factors: child's age, being fully potty trained (no pull-ups), how well they can 'handle' being part of the Club, and how full the ship is of children in that age group. We would not have been upset if they said she could not be registered as we had not officially paid for her to have all the Club privileges-- but it was nice that they gave her a chance and that we could leave her there a few times (for spa treatments, etc.).
I think your 'chances' of at least getting trial are pretty good but that is just my opinion. You and your child are always able to visit the Club and participate in the activities even if they are not registered (meaning you get a wristband, pager, etc.) We did this many times with our DD-- just came in with her to play. This age group seems to have more special visits from characters-- Mickey, Snow White and Daisy Duck all made visits when our DD was in the Club. Her favorite memory is "stomping with Mickey"!!!