Sometimes they will recover completely, although my experience is that, even if the quarter works, the milk on that side is never as good/plentiful as before and the ewe will need support to rear twins.
If the other quarter is ok then there's no reason why that side wouldn't work fine if you decide to keep her. Of course she would need help / one removing if she had twins.
If the affected quarter sloughs off, so long as the infection hasn't reached the other side, then I assume the other side would still work, but I haven't any experience of this situation.