There's probably only one real chance for this to happen: in the 1440s-1450s, with the Mongol tribes united under the leader of the Oirat, Esen Taishi. In 1449 Esen annihilated a Ming army and actually captured the emperor at the time. He then besieged Beijing, and was close to capturing the city, but was undone by a clever stratagem on the Ming's part (The Ming pretended to have left a gate undefended, then, when part of Esen's force had rushed into the city via that gate, they shut it, trapping the Mongols and splitting the army). Avert this, and Esen could well have taken Beijing. The conquest of all of China from there, however, is probably a tall order, especially considering Esen's complicated individual position; at this point he was technically only a prime minister-like figure under the Mongol Khagan, though he and the Oirat were the de-facto dominant element in the Mongol tribal confederation. His later usurpation of the Khaganate would be challenged by many Mongols due to his not being descended from Genghis Khan, and would lead to his downfall and the end of Oirat leadership of the Mongols. Have this usurpation somehow go more smoothly, however, and it might be possible to see a Yuan restoration under Oirat leadership in at least part of China.
After Esen fell, the Oirat collapsed into disunity; it would take an extraordinary leader to bring them back to preeminence. That leader did come later, in the form of Galdan Khan, active in the late 17th century. He received arms and limited support from the Russians, and was well on his way to his goal of reuniting the Mongols. By that point, however, the Manchu had consolidated their control of China, and Galdan found himself up against Kangxi, maybe the greatest of the Qing emperors, who foresaw the danger of Galdan's being allowed to succeed and moved against him with China's massive resources at his back. The Oirat stood no chance. Butterfly the Manchu conquest and have the Ming continue to stumble along into the late 17th century, though (or alternatively have them fall to Li Zicheng's peasant rebellion, with China left unstable and drained), and maybe Galdan or a similar figure could succeed in restoring Esen's Oirat-led Mongol Khaganate, and sweep into a weakened China from there.
One complicating factor with both of these scenarios is that, in each case, the only conceivable way the Oirat would have been able to conquer China would be as leaders of a broader Mongol confederation, rather than in an individual effort (as the commenter above me says, they simply didn't have the population base to pull it off by themselves). An Oirat victory would probably therefore be regarded as a restoration of Yuan Mongol rule in China rather than a new dynasty, as with the Qing (though this might not be as true for alt-Galdan as it would be for Esen, who actively claimed the title of Yuan emperor).
As to your question of whether this butterflies Manchuria being part of China, IIRC Esen's federation had power over at least some of the Manchu tribes, and it seems likely to me that a surviving Oirat-led Yuan would try to bring the Manchu as a whole back into the Mongol fold. An alt-Galdan scenario, however, could conceivably lead to an independent Manchuria, or one under Russian control, though really who knows.