Yes, but historically you can argue there have been examples of this kind of underhanded manoeuvre which have lead to huge global power shifts. A good example being the US having knowledge of Pearl Harbor, letting it happen and now 80 years later, Japan is still their completely subservient vassal state.
The US wasn't trying to provoke Japan into a war in 1941, it was trying to provoke
Germany into a war. At the time, it looked like Operation Barbarossa would succeed and that the Soviet Union would fall. If that were to happen, then Germany would have seemed unassailable in Europe. By that point, the US Navy and the Kriegsmarine had already started shooting at each other, and the last thing that the US wanted was to be distracted by a war with Japan. And then after Pearl Harbor, Hitler did Roosevelt a solid by declaring war first.
It's something that might be fun to think about, but it almost never happens in real life. Generally secretly helping the enemy like this is just not possible to keep as a secret, so leaders just aren't prone to it. And of course in this case, China doesn't need any more justification to wreck Japan. In fact, if Japan were to lose a war, not only would Japan lose the Senkakus, they'd likely lose the Ryukyus as well.