Yep, I would. But I guess it depends on the kids and their knowledge of the lay of the land as well as their independence and everyone's comfort level.
As for us, our 13 year old DS is an old soul and pretty fiercely independent. We recently traveled to Washington DC and DS didn't want to continue on with our next stop and asked to head back early to the hotel on the Metro on his own. Neither DH nor I were ready for that yet, but it made us wonder if we lived in the area if we'd be letting him ride the Metro on his own with friends by now. At home we let him ride his bike to 7-11 with friends. However, I also know kids his age that would never even think to want to split up from their parents in a big public area.
Anyway, at WDW he's not old enough to enter on his own yet, but after entry we will let he and his friend split up from us in the same park as long as we can check in and they meet us at the time we set. And in fact, DS and I took a trip on our own in January and we split up to do different rides one afternoon for about an hour. For us it is about letting the leash out little by little so total independence isn't a huge leap in a handful of years, and WDW is like a second hometown for DS so he knows his way around the parks like the back of his hand. It is a nice place to allow him a little independence.
BTW, some CMs do ask age at the gate. Last year at 12 DS and his friend went to another set of tapstyles from us and the CM made them point us out.