Yes, that's essentially what I did. The poultry store I frequent gives away free chicken breast bones, and they usually have a lot of meat on them. So, I simmer five or six pounds of them until the meat is just about done, take the meat off the breast bones which my cat and I enjoy as a snack, or which I throw into veg soup, or make chicken salad with, etc. The broth has a nice chicken flavor, but it's quite light, which is fine for some, but not all, applications.
At some point I'll make a second batch of broth, this time with some chicken thigh and leg bones, chicken wings, whole thighs and legs, and maybe some necks if I have any handy, and instead of using water I'll use some or all of the first batch of stock as the liquid, which has been waiting in the freezer. The results are superb.
Since the chicken breasts make such a light broth, even when cooked for quite a while, reducing the broth doesn't yield anywhere near the flavor as the second batch of broth.