Does fat leave meat when cooking?

For sure the beans will absorb some of the fat. However most of the fat will remain in the cooking liquid. Fat is lighter than water and much of it will rise to the top. You can skim some of this off.

If you cool and refrigerate the entire dish overnight, the fat will congeal and you'll be able to scrape off a lot more the following day. I do this for a lot of my stews and soups. You can't remove all the fat, there will still be some in the solid ingredients and in suspension in the cooling liquid.

If you want beans with the least amount of fat, cook them in water. If you use high quality beans, they will have plenty of beany flavor and will reflect the essence of the product. Ninety percent of the time I cook my beans in water (with some salt). This provides flexibility to add fat at the end for flavor to a portion of the beans and keep the rest fat-free, for example making refried beans (frijoles) the Mexican style with lard.