Just a fiscal point. The appetizers at Disney owned restaurants are usually on the "small" side and run anywhere from $5-$20 so you would be losing money on the DDP by ordering an appetizer for dinner. It would would be better for you to pay out of pocket and not get the dining plan. However, I assume you received the free DDP and that's why your asking.
Because it would actually be a profit to Disney, I can't imagine if you asked a server who then asked his/her manager that they would say no to such a request. If they understand that they could actually be making money on the transaction it's a no brainer. The only other issue is the fact that it costs less and the server would not get as large a tip but I guess you could throw in a few extra dollars if they work it out for you