I probably am going to get slamed for this but....
At best, a plug should be considered a temporary repair until you can get a proper repair. There are at least three issues when it comes to tires, air pressure and repairs. First, you need to maintain proper air pressure in tires. If you operate a tire with less than proper air pressure, you run the risk of the tire failing in ways you will not like. Nails and similar punctures are a source of air pressure loss. Occasionally, in the case of a nail in the tire, the tire will "seal" around the nail and have a slow leak. When you pull the nail out, you have a hole and a full fledged leak and the tire goes flat. Also occasionally, in the case of a nail in the tire, the nail does not penetrate the air chamber and you have no leak. In that case if you remove the nail you will not have a leak but you may have some other problems- more about that. One of the issues you may have with a nail in the tire is what kind of physical damage is the nail doing on the inside of the tire each time it rolls through the footprint. To know for sure, you need to dismount the tire and look inside. That gets us to the subject of repairs. When you get a puncture, you usually get two types of damage. One to the tire casing and the other to the air chamber. To do a proper repair, you need to fix both.
For the air chamber, a patch on the inner liner is usually correct. For the casing, a "plug" - not the rope plug or string plug you apply from the outside but a plug applied from the inside. The hole will need to be preped and a round solid rubber plug cemented in place to seal the tire body ply from moisture wicking from the hole into the body material. This moisture will cause material detachments and the tire will fail. A properly applied plug / patch combination will totally seal the puncture point and the tire should last. Just remember, if the tire has a speed rating, once repaired, it may lose the speed rating. To find out for sure, you need to check with the tire's manufacturer.