Even kids who behave badly are welcome unfortunatly. On our last trip we went to Narcoossee's and right beside us there were 5 or 6 kids at the table next to us with no adults. They were seated behind us and on the other side of us. The kids ranged from about 4 to 7. They were crawling under the table, throwing food at each other, playing with everything on the table, dropping plates on the floor, and every time a waiter went by they stopped them for something. One waiter had to escort one of the kids back from the restroom. I wanted to scream at the parents hope you're having a nice meal without the kids to bother you. I understand it's Disney and there are going to be kids there but at least sit at the table with them and control them some what.
With that being said that was the worst I've seen kids behave, mostly I've seen well behaved kids at all of the signatures I've been to.