Not always. Sept '06 we went into Columbia Harbour House. My diabetic mom looked for us a table while me and my husband ordered. The only adult dessert they had that day was listed as chocolate cake, so I planned to just order my mom the grapes off the kids menu. The lady across the register that was ordering just before me, apparently had the same idea. As she started to order, she just casually said she wanted the grapes for her meal, instead of the cake. The CM quickly told her that was not an option for adults, only kids.
I'd ask them to check with the manager if this still happens - everywhere we went that had fruit available they had no trouble letting you take fruit as dessert. (I think quite a lot has changed since September 2006, actually.) We were there just last week (5/19-5/25/2008) and saw many people getting fruit on the
DDP. The other option that is available at some counter services is Frozen Minute Maid lemonade which is wonderful on a hot day. Daughter subbed a milkshake for dessert at a couple of places, too.