If it is not the dominate dog, it shouldn't scare the others off. However, keep in mind, you want the dog to enter the trap, not walk up to the outside and piss on it. I do think it will be counter productive as far as getting a dog to enter the trap, rather than just piss on the outside and move on.
All of this is interesting. I've never trapped before, and 45 minutes ago I thought it would be a good idea to start setting bait in the near proximity of where the cage will be. So I took a large scoop of dry dog food and poured it on the driveway at the gate. Every bit of it is gone now. This was the big, dry chunk type dog food. Birds could not have eaten it. I wonder, what type of carnivore so quickly came to take the bait? Perhaps I will find out the very first day I deploy the unit.