Of course not! Dog waste is not part of a healthy ecosystem and dog owners are expected to remove dog waste – regardless of where it falls. If a dog goes bushwhacking and lays one down, then the owner needs to go bushwhacking and pick it up. Trash receptacles are often placed 100+ yards up trail from a trailhead, but if your dog relieves itself beyond that, do the responsible thing and pick up/carry out the waste.
Please do not leave a “doggie bag” on the side of the trail. More often than not, they are forgotten and left to rot on the side of a trail. Bring extra waste removal bags just in case.