Yes, and yes. Sensodyne contains fluoride (which is a neurotoxin; such as lead, cadmium, and arsenic). Therefore, I would say yes, it is bad to swallow this toothpaste, leave any reside on your teeth, or even to use it at all.
Concerning other health effects; I consider that ingesting only food is a critical step toward optimum health. If the toothpaste were composed of things resembling food, such as hydrogen peroxide and baking soda, then toxicity would be of nil concern. You could also use plain hydrogen peroxide and omit the baking soda. I use only straight 3% hydrogen peroxide. It seemed rather strong the first many times I brushed with it, leaving many small and mostly painless white spots on my tongue and gums, but now it seems largely comparable to plain water.