We used the open house times a lot with our almost 2 year old DD on our cruise in November. Our 7 year old DS adores his little sister, and didn't want to go without her, so we spent a fair amount of time there with both of them. She is potty trained, but not potty independent, and she is small for her age; there was no way we or they were going to consider letting her go alone.
We did use the nursery several times for her. She is very advanced for her age and used to hanging out with older kids, so she really preferred the Oceaneer's Club. She was climbing up the pirate ship and going down the big slide in the Club fearlessly; she adored it. She also enjoyed doing the crafts in the Club. Honestly, I think she liked it better than her brother did. She put up with the nursery. I think she liked the attention from the adults, and they let her eat, which is always a hit, but she preferred the activities in the Club.
She'll still be 2 on our next cruise, but she'll be within a month of turning 3, and I'm going to really try to get her in the Club. If the nursery was boring to her at her 2nd birthday, I can't imagine how she'd put up with it right at her 3rd. I suspect she'll still be small, which may worry staff, though.
As others have mentioned, my understanding is that if space is available, they will work with the families of potty independent almost 3 year olds. I don't know how close to 3 the child has to be, and I know they evaluate on a case by case basis.