No. GAP insurance won't work to put loss of value back on your vehicle; it does not cover this type of situation.
GAP insurance is there to pay the difference between the actual cash value of the vehicle paid out by your car insurance company and the current outstanding balance on your loan or lease, after a total loss situation has occurred.
It does not appear that the hail damage to your vehicle resulted in your vehicle being totaled out, so GAP insurance could not be used even for the purpose it is meant for.
Your vehicle received hail damage and you now expect that repair being listed on Carfax and other vehicle history reports will bring down the value of the car if you go to sale it in the future; this is what we refer to as diminished value.
The basic definition of diminished value (also known as diminution in value or DV) is the difference in the market value of a vehicle without an accident history and the market value of the same vehicle with an accident history. In your case, the hail damage history is what you are worried may affect your car's value and would like compensation for that.
In a few states you can make a claim with your primary car insurance company, not your GAP insurer, for diminished value.
In most states, car insurance policy language is allowed by the state to exclude payments for diminished value claims for first party claims. This means that though your hail damage was paid for by your Comprehensive coverage, it is unlikely your policy allows you to claim for the lower value your car now has.
You can however read through your policy and speak to your agent to see if DV is something your insurance company and state allow you to make a claim for and if so how to go about doing so. Likely it will include showing that your vehicle is now worth less even though the hail damage was repaired.
If your agent is not able to explain to you what to do in this situation or fulfill your car insurance needs, contact a CarInsurance.com agent and they can explain not only insurance terms and explain claim procedures but also tell you how they can get you low cost car insurance.