Having designed, manufactured and sold tyre repair materials for the last 25 years, I feel qualified to comment here.
If the 'plug' as you call it is a branded 'mushroom' or 'combination' plug patch and was fitted from the inside of the tyre during a full inspection, by a reputable repairer complying with the relevant British Standard, the repair will be fine, whatever you do with the car.
Having said that, if that was the case it wouldn't have leaked after repair, even for a short time.
On the other hand, if it was an externally applied string or rubber plug you would be well advised to have the tyre properly repaired or scrap it.
Just today I was advised of a fatal incident in the UK being laid at the door of just such a repair. I wouldn't like to hear of another.
If the 'plug' as you call it is a branded 'mushroom' or 'combination' plug patch and was fitted from the inside of the tyre during a full inspection, by a reputable repairer complying with the relevant British Standard, the repair will be fine, whatever you do with the car.
Having said that, if that was the case it wouldn't have leaked after repair, even for a short time.
On the other hand, if it was an externally applied string or rubber plug you would be well advised to have the tyre properly repaired or scrap it.
Just today I was advised of a fatal incident in the UK being laid at the door of just such a repair. I wouldn't like to hear of another.