[Note: I thought I had hit the send button on this around noon today, but rushed out before having done so. Some of this has been covered by others but I'm leaving it "as is."]
Yes, you can. No, it will not be fun. Been there, done that.
If it is leaking, you really have no choice. If you just believe it's stuck, then I'd disconnect the cable and try to manually unstick it.
It's also not uncommon for the securing screw for the cable to the tap lever to become loose and the cable just slides through. You may (and I do say may) have a worst case scenario where the tap was frozen, the securing screw not loose, and the end of the cable will now be badly damaged from having been pushed and pulled in place so many times.
This was not one of Crewe's best design choices.