Well, let's not forget the plates or the cutlery, either. Or the trays...And even when they did, they had ordinary celery on the same plate ("Man Trap")... Somewhat eating away at the theory that everything on the plate came from a primitive synthesizer of some sort.
"Eating away"...no pun intended, I'm sure!!

Oh, the tribbles could have been already contaminating the food slots and just waiting for the food to be replicated. It's not as if the process of replicating a meal is somehow hazardous to the immediate vicinity - our heroes are always sticking their hands into the replicators before the process is properly finished. So a tribble could easily wait in the comfy slot for its next hot meal...
That is, of course, a good point, but as far as we could see there was NOTHING left of Kirk's chicken sandwich by the time he got it (just the pickle). Unless the tribbles consume food at warp speed, I don't think they could have eaten the whole sandwich in the time it look for the synthesizer to chime and open the yellow door.
