I started chili and added uncooked, rinsed bean bean to my meat and base base will the beans cook?

The beans can cook, provided you add more liquid to the chili base to rehydrate them. You will also need to give them a lot longer to cook- several hours, more than likely, at a good simmer on the stovetop. If you do not provide extra water to rehydrate your beans, they will suck up all the moisture that is available to them. If there is not enough liquid to fully do that, they will not cook- and your chili is likely to burn.

Most likely not. There can’t be enough liquid in the chili to properly hydrate the beans.