No. The Dalai Lama is the head of the Tibetan Government in
Exile. He is not even the head of any of the 4 schools of Tibetan
Buddhism (Sakya, Gelug, Nyingma, and Kagyu). In fact, the 14th
Dalai Lama's political role in Buddhism has cause many problems
within Buddhism. He has caused huge divisions in both the Kagyu and
Gelug traditions. Search 'Dorje Shugden Controversy' and 'Karmapa
Controversy' on Google or click on the related links below to learn
more about problems in Tibetan Buddhism created by the 14th Dalai
Lama.