Agrees with cmason. Never hurts to cover it. I have leftover black chaircovers from my wedding that I cut a hole in, they slide right over it. Before I remembered I had the chair covers, I'd wrap a towel around it and secure it at the neck with a rubber band. Of course I'm so "pack for bear" minded that I even cover over the few inches of exposed neck space on my demijohn.
Ounce of prevention.... even if it's overkill, is still an ounce of prevention.