Providing you provide details of the other party you'll be covered. Most (but certainly not all) insurance companies and policies these days have a no fault excess policy so if you're not at fault you won't have to pay anything.
I had the rear door of my car backed into at the supermarket a few years ago and the person who did it left no details however another witness gave their details and the rego of the truck. I rang AA insurance with these and had them call me back a few hours later approving everything and waiving any excess, I was quite impressed how quickly they processed things.