What are some arguments to support the thesis that Peter the Great was a successful absolute monarch?
Peter the Great was indeed a successful absolute monarch. After his Grand Embassy to the West, he single handedly transformed Russia into a Western Country complete with Western Dress and Western customs. Also, during the Great Northern War, he captured land on the Baltic to give Russia it's "Window on the West," a sea-port which he built and named for his patron saint: St. Petersburg. His palace there, The Peterhof, can compare with Versailles in many respects. Peter tolerated no dissent, harshly crushing the Strelsky Revolt which hoped to reverse his movement towards westernization, and even ordered the execution of his own son, Alexis, after Alexis was involved in a threat to overthrow him. His sister, Sophia, who had been his regent, was involved in the Strelski revolt, and was confined to a convent for the rest of her life. By acclaim of the Russian people, Peter was named, "the Great, Emperor of Russia," the first Russian Czar to bear that title.
I find Peter the Great both interesting and intriguing as a historical figure. If my criteria for his "success" is simply whether he was an effective absolute monarch, then I agree with you that he was.
Consider the fact that he faced challenges to his rule and his empire from both within Russia (see his fight against the Cossacks in The Bulavin Rebellion) and from without (Philip XII of Sweden's invasions of Russia) and the fact that Russia truly became an empire, with a much more modern army under his rule, and I would say he was successful.
He was also brutal with his challengers and his enemies, something else that has served autocrats well in the past, and certainly did in Peter the Great's case, and he bulit the city of St. Petersburg on the River Neva.