Depends --
A high protien diet and maintaining prestine water (3-4 PWCs a week or even daily) will go a long ways towards helping the fish not only recover, but prevent any secondary infections, which is the main concern ATM.
The second conern would be, what caused the fin loss? ...and to remove/prevent this from occuring.
Also, if the fin damage goes beyond the fin-tissue and has affected/damaged the boney structure within the fin, then the odds are no, it will not grow back.
Lastly, there are Meds available to help treat and regrow soft tissue damage, but I tend to think clean water is just as effective IMO.
Do you know the cause?