Sure, but keep in mind it may count against you similar to an accident where you're 100% at fault since they have no way of recouping the cost. Depending on your track record you may see an increase in your premium.
I got one of those Duplicolor kits. It comes with body putty to fill in the scratches, which you let dry. Then you prime it. You need to buy some paint in your color and apply that. Then you apply the clearcoat. Works great, includes all directions, sandpapers, pre-wipes, etc. All you need is the kit and some base paint in your color.