Credit card rental car insurance deductible?

So I am planning to rent a car with a credit card (MasterCard or Visa) with a rental insurance policy benefit and I have full coverage with Geico ($1,000 deductible). My question is if I were to rent a car and decline the CDW or LDW offered by the rental car company and then get into an accident, would Geico pay everything above $1,000, and could I collect the deductible from the credit card policy?