I did it for a few years, when we had a regular truck.  I did notice my dogs were not happy riding in the back.  And once the "smell" of exhaust got my attention, the  next truck, had a extended cab and the dogs rode there.
You could put a battery CO2 meter back there and check the readings.  Be sure the meter has a "history" record.
I won't do it again.  I think the dog is safer and better off by having you remove the canopy, if you want the dog to ride back there.