Cheap pots tend to get stuck like this
Realistically, yes.
Shouldn't cost more than $10 to do if you can solder. No need to remove the strings even (if you are careful!). Slacken the strings, remove the scratch plate screws and wiggle the scratch plate out taking care not to break the earth to the trem block or the screened lead to the output socket. Put a towel over the guitar body so that it doesn't get scratched. Replace each pot one at a time (so that you don't confuse the wiring). Use a 50 watt soldering iron to make a good connection to the pot cases. Should take around 30 minutes.
While you've got the scratch plate out, it would be a great excuse to upgrade the pickups, fit a coil tap, fit some screening, whatever
