Does the food bank give out cat litter as well as cat food?

Yes, they do. As long as they have it of course. They do have cat food, both dry and wet, more often than not. They also have pet toys, leashes, harnesses, bowl's, and the such.

I have never seen them giving out cat litter but they might give out cat food

We don't purchase cat litter but we do give it out when we get some donated. Looks like we have one container on the pet food shelf currently.