If you put enough powder and ball through the rifle I am sure it is possible. Personally I have found that most of the time you find that the barrels you think are worn out are damaged due to poor cleaning habits.

If you are unable to obtain any kind of accuracy with a rifle barrel at all, then it is time to give it a real hard cleaning. I thought I wore out a .54 caliber Renegade barrel once. Found out it was poor cleaning habits. Take the barrel and give it a quick lapp job or take some J-B Bore Paste and scrub the devil out of it. Then see if the accuracy returns.

Since you have a T/C Hawkins you can replace the barrel with a Green Mountian IBS barrel. Or you can contact Thompson Center and see if they will take a look at it for you. First though, I would give it that good cleaning. It brought my Renegade back and I am still shooting that old devil.