If the Mongols themselves ruled Russia as well as China (or from Russia and Scandinavia to and including China including Siberia all the way to the Bering Strait) then yes, their policy would start out very much Chinese but with some major departures. For one thing, Gelugpa Buddhism would play a major role in how such a Mongol Dynasty would define itself.At the very least, Buddhism would be more important and have more patronage in China than it would have had at any time since the Tang.
Secondly, controlling the "barbarians" would mean two things. The nomads the Mongols would not already control and that they would need to control, such as the Kazakhs and the Tatars and the Uzbek and the Turkoman and maybe the Aimak and the Tajik and the Hazara are Muslim. The Mongols would be trying very hard to get them to either accept Gelugpa Buddhism or settle someplace else like the Ottoman Empire or Persia or India or be killed off. The other set of relations would be with Muslim --and Christian European states, to whom the Khanate would appear both profitable, threatening and a potential alliance partner. What would "use barbarians to fight barbarians mean for a China either bordering on Russia and Sweden or Poland and Austria and Sweden and able to play European nations against one another? How would that affect European history? For that matter, how would European history have been affected if the Chi'en Lung Emperor had driven the Dzungars into Russia and decided to keep Siberia and stay on Russia (and Sweden's Volga and Northern Dvina frontier, becoming a player in European politics much as the Ottomans did?