I no longer have tubed tires, but during the days I had, and especially in my bike, I never repaired a puncture, I always used to replace the tube. This is advisable, since in the short (sometimes long!!) distance that you will take to come to a halt after you have lost pressure, the tube will have suffered damage in areas other than the puncture point due to the running in flat condition ... it is a perfect recipe for future blow-outs.
BTW, any ideas on the limit to the number of punctures you can repair on a tubeless, before you should go for a new one?