No way would I ride with a dog on a leash. Disaster waiting to happen.
You have to know your dog. Herding types would be the perfect bike dog- they would try to keep you in line. I have two big greyhounds. Their idea of a run is a 40 mph sprint for 500 yards, then collapse and cool down. They amble when they walk.
If you do it, consider the animal first. My dachshund would do his best to keep up until he was completely exhausted. He had the heart of a champion & the body of a weiner dog.