I understand the second part of your post. But if a short or fault were to occur in the pump, having it off would prevent an electrocution, right? I'm not including electricity from the ground.
For the first part of your post, I meant the grounding wire for the pump. I went outside and looked at the wiring again, and it looks like there is a bare ground in the conduit that comes from the pump to the electrical panel. That ground wire is about 18 gauge, which is smaller than the hot and neutral wires (it's common for a smaller ground wire; to trip the breaker).
So, it looks like that green wire coming from the pump (that I originally thought was the ground wire) is the bonding wire. It is about 8 gauge, and goes directly into the ground (hopefully to the pool). It is also attached to what I now know as the bonding lug of the pump. I guess the person who installed that bonding wire used a green insulated one.
So, to recap, I've figured out that the grounding wire coming from the pump is actually the bonding wire. The pump has an actual grounding wire in the conduit coming from the pump. The green bonding wire is what threw me off. That leaves me with my question from the top of this post that I'm assuming to be yes, because the switch disconnects the hot when off.