I think the CS issue may be that you are misunderstanding what you get with a CS credit. A CS credit is good for one entree OR combo meal (so sides are not included), a drink and a dessert. Any of the CS places that offered you a side were very generous and going beyond what the plan offers. So a sandwich or salad do not get a side since they are entrees. A cheeseburger combo would come with fries and so that would have a "side"
As far as the OP's question--I doubt it but it never hurts to ask--expect some places to let you and others not to.