The first thing you should do, in case you haven't, is file a police report. That way you have legal proof of the occurance for your own records... It's not really mandatory, but if they catch a white car on another hit and run, or getting pulled over for something else with marks that line up to your car it would be good. It's unlikely, but hey, why not?
Second, as someone said, get an estimate (multiple, if you want.) and give Geico a call if the deductable is less than the estimate. I don't believe that insurance companies hold hit and runs against you. (If you had an outstanding number they might begin to think that YOU are the person doing the hit and runs, but that's not what we are talking about.)
So basically, if you can get any money from insurance, you'd be dumb not to, because that's why you pay for insurance. Most people pay tens of thousands of dollars in their lives for insurance and never make a single claim. Pretty stupid if you ask me.