Yes, as the great Lama, Kelsang Gyatso ,explains, Manjushri (the Buddha of Wisdom), Je Tsongkhapa and Dharmapala Dorje Shugden possess the same mental continuum. Historically, Je Tsongkhapa manifested as a great pandit and teacher to restore the purity of the Buddha's teachings and to bring in a new renaissance of Buddhism, at a time when the Buddhadharma was declining. Then Dorje Shugden, arose as a Protector to prevent the teachings from degenerating and disappearing.
Kelsang Gyatso also reminds us that at all times, beings with the same mental continuum as the Buddha, will appear to ensure that the Buddha's teachings continue to spread and to prevent the teachings from degenerating. These are the Spiritual Guides that guide us unfailingly on the path to liberation and full enlightenment.
We can also see the same mental continuum in the Incarnation Lineage, from Mahasiddha Biswasa ,Sakya Pandita, Buton Rinchen Drub, Duldzin Drakpa Gyeltsen, Panchen Sonam Drakpa, Sonam Yeshe Wangpo, Ngawang Sonam Geleg Pelzang to Tulku Drakpa Gyeltsen. Duldzin Drakpa Gyeltsen was said by Kyabje Trijang Rinpoche,(in Music Delighting an Ocean of Protectors) to be of the same mindstream as Je Tsongkhapa. Hence, his subsequent incarnation lineage up to Tulku Drakpa Gyeltsen would be of the same mindstream as Dorje Shugden.
Hence, whichever way we look at or trace it, the mental continuum of Je Tsongkhapa is the same as that of Dorje Shugden.