It works fine, with caveats

First, that the chicken parts are likely to give up their flavors and collagen sooner than the beef bones.

Second, that you can't make chicken broth with beef parts, but you can make beef broth with chicken parts. Even the best chicken is going to be overwhelmed by anything beef mixed in. So you'll get texture, mouth feel, from the chicken, but you'd hate to have an absurdly sensitive palate to taste the chicken in it. It isn't impossible, but chicken, and even pork get dominated by beef. Pork can hold up a little better, as long as it's the majority of the bones, but I wouldn't say it tastes the same as a pork only broth.

But yeah, it'll taste just fine. Bone broth is yummy, period.