I love having a beat to hell putter in the bag. If you start with a nice stable putter like a bb aviar or wizard, a really beat one will have a nice amount of turn without getting squirrelly. Lots of older players have putters in their bags that have been used for a decade, it's pretty hard to beat a putter so much that it's unusable.
I have seen such putters. Generally speaking they don't beat in too much that you can't at least putt with them. As fart as driving with them thats another story. Drivers on the other hand, once they get too beat, they are too understable to do much good other then rollers.