I have to confess that I'm a bit confused by what you're asking. Surely, if a queen has been superseded, she's dead? If you mean the daughter of the superseded queen, I wouldn't have thought there was anything wrong with the queen per se. It's more about what you intend to do with her. You said "breeding" but I think you mean "rearing" since breeding has a specific meaning and requires that you control both sides of the ancestry. I don't think you mean this - you've just used the wrong terminology but this has made it more difficult to understand exactly what you're asking.
I don't necessarily think there is anything wrong with the daughter - she will be genetically the same as her sisters - the workers. So, if the mother was control-mated, the queen will be good to use - as a drone mother if open mated or a queen mother if she is also control mated. I would add the provisor that queen mothers should also be performance tested if they're part of a breeding programme - but if you just meant random mating, then she'll probably be no better, or worse, than anything around you -it's pot luck!