I have had similar experiences with all 3 of my children.
All of the kids loved their pull-ups so much that they became lazy about going to the potty. Also, my current toddler has an absolute fit if the room's cold while her bottom is bare.
Also, whether or not they have on pull-ups or cloth underwear, all my kids needed constant reminders until they were about 4 or so.
It sounds like you already have him potty trained.
If you are worried about accidents, don't be worried, the daycare should be able to understand that.
As a matter of fact, ask the daycare to specifically define their expectations to you. And let them know your situation and ask for their feedback. They deal with this all the time and are "experts" on it. You know?
There is a big difference between having accidents and totally being clueless about going to the toilet. I can't see that they'd keep you from having your child attend their program.