Patch, yes. Plug, no.
The proper way to have a tire repaired is to patch the tire from the inside and fill the puncture hole. Do not have your tire plugged. Ever. Plug repairs do not involve taking the tire off the wheel for a proper inspection. A plug is simply inserted into the punctured area, making it unreliable. Insist on a full inspection. Have your dealer demount the tire, internally and externally inspect it, and patch and fill the repair on the inside of the tire.