I don't ever see anyone do it, but if it's big enough and the drive thru doesn't have that curb that keeps you from pulling out. why not? I went through the mcdonalds drive thru with the trailer yesterday cause their wasn't anywhere to park.
I honestly wouldn't care if I were in the drive-through also, provided you actually drive through at a sensible pace and don't do a bunch of backing up/pulling forward mess. It's not like your trailer made an order or will take any longer for me to get mine because of it.