Will it work if the caterer just drops off the food?

I wouldn't have them arrive later. The burners should be fine to keep it warm, that's the entire purpose for using them. If all there going to do is drop off the food then you can always rent the plates & utensils from the same place you're getting your chairs & linens from. They can come by, set up the burners, place the trays on there & that's it. I wouldn't stress over it too much. Most people don't eat before they attend an event so they'll be expecting food to be served right after the ceremony. It's okay to start with appetizers while you're off taking pictures & then move onto the main dishes but I would definitely not have a buffet with veggies & sushi. Everyone's going to fill up on that & probably not eat most of the food when it finally arrives.