Your best bet is to call GEICO and add full coverage. Tell them the scenario - that you are going on vacation and want to be sure the rental car is covered under your own policy with a low deductible and to please quote you the policy change price. If you obtain coverage directly through the rental company most times it is around $20/day on top of the normal rental charge, so if you can get the coverage through your own private policy it would be better. (Especially if you actually need to file a claim.)
Take a camera with you when you rent and take photos of the car from all sides and angles while the rental agent is there with you. This may help cover your butt later if they try to claim damages you didn't do.