Conceivably it could but the stylus would have to hung up in a major gouge in the record. Just to give you an idea, I picked up and old Dual turntable from the 1970's at a junk shop some time back. It had what looked like a Shure V-15 Type II from the same period. I took the Shure off and mounted it to a current turntable and I haven't had any issues whatsoever. I've done this with several other older carts too. If the suspension is worn, you know pretty quickly. If you make it through a few sides without any issues, I would think that the cart should be fine.
Just to be on the safe side, I'd use an older, less valuable piece of vinyl to test your cart on. That way if it fails, you haven't scratched a record that you really wanted to keep pristine.