No, if there is no primary insurer paying out the actual cash value (ACV) for your totaled vehicle then GAP insurance will not normally be able to be used.
If you were at-fault in the accident that caused the accident then you would need collision to cover your vehicle and pay out ACV so that your gap insurance policy could then pay out the difference between the ACV amount and the balance of your loan or lease. If you only have basic liability coverages then your car was not covered by your insurer and thus they would not pay out ACV.
If you were not at fault in the accident and thus are making a claim against the at-fault party's property damage liability coverages then once the third party claim for your totaled out vehicle is paid out then your gap insurance provider should pay since there would be actual cash value paid out on your vehicle by the other person's insurance carrier.
Gap insurance is there to pay the "gap" between the actual cash value of a vehicle determined to be a total loss and the balance of the loan. Without the ACV being paid out there is no "gap" just the entire amount of your loan, which is not what gap insurance is meant to cover, as the terms of your gap insurance likely state.
If you are in a situation where you only have liability coverage on your totaled vehicle and want to see if your gap insurance could help you in any way, you should read through the terms of the policy and speak to an agent of your gap insurance provider.