I think it just varies by restaurant. When we stopped at the Cantina on our 'snack and drink around the world tour' (LOL), we ordered nachos in the beer line on the side and they said no substitutions at that counter - it was like it's packaged. But I think by the way he said that that they do make changes if you order at the real counter and not the beer line. A lot are prepackaged, just like McDonalds, but you can still request and wait for a special order.
So, depending upon how they get the food, you'll have to just ask.
(at Panera Bread the chain restaurant, you can make changes to all but the panini's because of how they receive them predone and frozen - so I just know I have to pick off tomato's on the panini's there. I think the same is true for the counter service at WDW - just depends on the food and how it comes packaged to them)