No, use it. Drain the broth into a container (if it's still hot when you do this, drain it into Pyrex or other glass). If you leave it in the crock, it stays hot a lot longer, which you don't want. You can strain out the chicken parts, or you can just leave them in there for great soup. Let the broth cool, then put the glass container in the fridge to chill. The fat will congeal on the top and you just scoop it out with a big spoon or a ladle, and discard it. The broth can be used for soup stock as it, or strained for adding to something like rice, quinoa or couscous (any grain that absorbs all the water during cooking). The vegetables don't ruin it - most potatoes will make it a little thick or cloudy, but that's okay. Just think about the seasonings when you are adding it to, say, rice. It might taste much better with a roast chicken and rice dinner than with a Chinese stir fry rice or Mexican rice. But that's because of the herbs and spices, not the chicken broth itself.
Chicken broth and vegetable broth can be used in a zillion recipes, and can usually be interchanged. Freeze leftover, defatted broth in containers or ice cube trays and defrost as needed.