Well, sure, it's possible... but you'd need to get the sandwiches, then get from Downtown Disney to DHS (easier if you have a car, but not particularly convenient - and don't forget, many of the EoS sandwiches are either heated or spoilable, depending on the length of time between prep and eating, as well as the outside temp).
You'd need to allow plenty of time to get from DtD to DHS, then park if necessary, enter the park, get to the Fantasmic! Theater in time to get seats, then wait for the show. I assume this is the show to which you refer?
It just seems like a LOT of extra effort. The Counter Service options at DHS may not be gourmet, but it's not horrible. It's food.