Non-owners policies may have restrictions, such as you cannot own a car or have one available to you or your household that you could place auto insurance on, but these will differ from one insurance company to the next. To find out what Geico's restrictions may be for their non-owners policies you would need to contact them directly.
In general a non-owners auto insurance policy offers coverage for not just rental cars but any car the insured driver wants to drive and does not own. If you, the insured driver, borrows a car from a friend and then were to get into an accident, your friend's insurance would be the first to cover the losses. But if the accident was your fault and the damage to the other driver's property exceeded the liability limits on your friend's policy, your non-owners insurance policy would cover the excess, up to policy limits.
If you do not have a car now and plan to get one in the future maintaining a non-owner auto insurance policy will help give you prior insurance history and should help you receive better premiums rates when you do purchase a car and want to cover it fully with insurance.
With non-owners it should cover your liability needs for a rental car even if you are using it everyday since this is not a car that you own or could place insurance on since it is owned by the rental company. If the car was owned by a family member and you drove it everyday then an insurance company may say that this was too frequent and that you would need to try and place coverage on that car, even without having insurable interest in it.
Keep in mind that non-owners policies usually cover an insured with liability, medical payments, and perhaps uninsured motorist coverage. Non-owners policies usually do not insure for comprehensive, collision, towing reimbursement, or rental reimbursement coverage. So if the rental car was in an accident that was your fault then your non-owners policy typically would not cover the damage to the rental car or the fees that the rental agency would place on you for the time in which the rental car was out of service for repairs.
To protect the rental car in this way you would still need to purchase from the rental agency. Most car rental companies offer a Collision Damage Waiver (CDW) also known as a Loss Damage Waiver (LDW). A CDW / LDW is not insurance; it is a contract offered by the rental car company.
This contract shifts liability for collision damage from the person renting the car to the car rental company. Collision damage is usually defined as any damage to the rental car resulting from an accident. The CDW contract protects only the person signing the rental contract. Other persons not mentioned on the CDW are not covered when driving the rental car.