No, the repair fee will go on your insurance policy because insurance is not on the person driving it but on the car. Also, chances are your auto insurance rates will go up if you file such a claim.
Therefore, make sure your friend has a good driving history before you give your key away.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.