Your going to get A LOT of different opinions and reasoning on plugging v replacing a tire, and you will probably hear A LOT of people tell you stories about how they plugged a tire and rode/drove it for thousands of miles with no problem.
But, I'll give you my opinion and it's worth every penny you paid for it.....
I worked in the aftermarket tire industry for 30+ years and received factory training from virtually all of the leading manufacturers of tires. ALL of them advise against plugging tires and using it as anything other than a temporary repair. Some people are going to say that this is just so they can sell more tires or to protect themselves against frivolous lawsuits. But if you look at the numbers of new tires sold every year v the number of tires that get punctured, it's such a small small percent of total tires, that claim goes out the window. NO shop could make it just selling replacement tires for those that get punctures, and no manufacturer could survive either.
What WAS shown to me, and reinforced by actual observation in shops I managed, was the INSIDE damage that occurred to countless tires that were punctured, but was NOT evident from just inspecting the OUTSIDE of the tire. In virtually everyone of these examples the tire would have been a serious safety problem if merely plugged and let go down the road. Even in the case of a small screw that goes into the middle of the tread there is the distinct possibility of the air loss causing overheating and damaging the inner liner of the tire....the inner liner being what really holds the air in the tire. Longer items have been known to actually reach the inner sidewall of the tire and cause the liner and body cords to be damaged. Items that go into the tire and are not removed can also cause this type of damage.
The ONLY acceptable type of tire repair as a PERMINENT solution is to remove the tire from the wheel, give it a though inspection and then PATCH/PLUG the tire from the inside, if no damage to the structure of the tire has been done. If ANY damage is found, the tire must be replaced.