I have has flat repairs on both sets of tires over the years. This topic is always debated.
They remove your tire and inspect it. Since you were not driving on a flat it should be good and the nail is in the tread. It goes by different names, but my tire shop calls it a stem patch. It is put in from the inside of the tire. It is not the plugs you see at auto parts place that are inserted from the outside.
Make sure that they have the machine that does not touch your wheels or they can get scratched. Find out who the local Boxster 996 owners go to.