Say the Qing survived the Xinhai revolution and the Qing was able to regroup and reconsolidate power after the 1910s and 1920s, do you think Japan would still have had the guts to invade China in the 1930s to face a united Chinese Qing military (as opposed to the warlord period and the divisions of the beginning of the Chinese civil war?).
Would the war in Asia have been averted?
The war in Asia won't be averted, but the Chinese would still win due to logistics and morale, plus they're still defending their homeland, but would be less successful due to increased disunity [hatred of Qing, not political warlords and corrupt politicians plus rival governments] between the Chinese military officials and politicians. Maybe the Japanese would try and pose themselves as 'liberators' by placing an ethnically Han Chinese [puppet] regime to try and gain credibility, but it won't be successful. The Japanese might still have the guts to invade China, especially because even with a more stable government, the Manchu leaders were known for corruption and backwardness and there would be many anti Qing Chinese people.
Of course, that's assuming the butterfly effect won't prevent the Sino Japanese War.