Theoretically, no - because the signal is carried down the centre conductor, and the overbraid is a shield/ground. However, if you've managed to strip a spot bare of shield, you might pick up some spurious signals.
If the shield is intact, you can probably get away with taping over it and resealing it that way (or applying some heat-shrink, if you can get it there.) Me being me, I'd replace the thing anyhow - but I'd have also had a grommet in the hole to protect the wiring (I'm cranky that way - never run an unprotected wire over an uncovered metal edge!)