Yes and no at the same time: you could say the people brought down the Ming government in Beijing in 1644. That's the conventionally-used date for the end of the Ming, but the Ming loyalists held out in the south for a few more years afterwards until conquered by the Manchu Qing. The thing is, the south was largely spared the rebellions of (roughly) 1639-1644. So if the Manchu are defeated at Shanhai Pass, I think there's a good chance that the Ming might survive in the south. However, the historically disorganized Ming remnant might also be conquered by the Shun.