I ran my last tire to death (Angel ST) with 4 sticky rope plugs in it at the end. Towards the end, the tire was so thin, it broke the seal on the plugs, so I added just a touch of Green Slime (just enough to coat the very center of the tire, but nothing else).
The way the TPMS takes over the display, you will know right away when the tire gets below 32 PSI, well before it becomes a major handling issue, so just run it. If it gives you problems, then swap it.
I found mine didn't leak a bit until the tire wore to the point it became thin. I added the other 3 just to finish out the last couple of weeks of the riding season because by then, gravel was poking holes in it.
If the puncture is in the center area of the tread, I would have no problem running a plug on your tire for the life of the tire.