Dear Emptymountains,
As far as I know, no. The first person with the title DL was the so called 5th, and they imputed the same title to a line of reincarnations going back to Venerable Gendundrup, who was one of Je Tsongkapa's disciples. None of those holy beings --the first, second, third and forth-- had anything to do with the title DL during their lifetimes.
After I wrote the previous message, I thought that I should've said also the following. I don't think it would've been incorrect to say that Tulku Drakpa Gyeltsen was a reincarnation of Ven. Gendundrup, because all of those holy disciples are like emanations of their Teacher insofar as they've gotten all his attainments. But let's not forget that primarily Tulku Drakpa Gyeltsen is the reincarnation of Dulzin Drakpa Gyeltsen, another of Je Tsongkapa's disciples, the one to whom for the first time the great Protector of Tibet requested to become a special Protector for the Ganden teachings. This question was going to be asked two more times that I know of, one to Panchen Sonam Drakpa, and finally, just before the time came for him to arise as our Protector, to Tulku Drakpa Gyeltsen.
If there are errors in this information, they come exclusively from me.