I agree with blowing the feed line with steam prior to closing the drum, which is a very good practice we have developed over the years at our Coker.
Keeping the quench water running into the inlet line during drilling would only work if you have individual quench water controllers for each of your coke drums. Usually on a 4 drum Coker you have 2 drums coking, 1 quenching while the other is being drilled.