I also like Gaz’s answered to Tsongkapa. It’s very knowledgeable and explained very clear and easy to understand the linage of Dorje Shugden.

I pray that, may the doctrine of DS continuously to benefit and touch more and more people in the very near future! OM BENZA WIKI BITANA SOHA!

During Tsongkhapas time, Dorje Shugden was actually a monk and one of Lama Tsongkhapas disciples. This monk was called Dulzin Dragpa Gyeltsen. During one of Tsongkhapas teachings, Dulzin was present and receiving the teachings. A white dove flew above the sangha and circled the hall.

After the teachings Dulzin approached the white bird who turned into a young boy. He asked him why he was disturbing Tsongkhapas teachings. The young boy (who was Nechung in disguise) asked him if he (Dulzin) could become an uncommon Protector of Nagarjunas view. Dulzin promised he would be, and the young boy disappeared.

A few incarnations later, when Dulzin was now Tulku Dragpa Gyeltsen, Nechung returned to remind him of his promise to become a Protector. Tulku Dragpa Gyeltsen manifested not remembering, so Nechung took some rice, blessed it and had Tulku Dragpa Gyeltsen eat it.

After eating the rice, he remembered the promise he had made as Dulzin and say okay, he would fulfil his promise but he no longer had any wrath in his mindstream in order to become a Dharma Protector. Nechung said not to worry, he would create the causes then disappeared. After Nechungs machinations, well Tulku Dragpa Gyeltsen was murdered and arose as the Protector Dorje Shugden.

This is a MUCH abbreviated version to the full story told here – http://www.dorjeshugden.com/downloads/texts/first-ever-dorje-shugden-comic-book/

So the short answer to your question? Dorje Shugden arose hundreds of years AFTER Tsongkhapa had entered clear light (passed away) so there is no way Tsongkhapa couldve practised him.