Not likely, especially when it is probably going to start over some sh... er, incident in the Middle East.
The hat trick will be to fight such a war between some combination of these powers (and their allies) and keep it from going nuclear. The US force structure is no longer large enough to fight both of them full on at the same time. (A problem that is not entirely Obama's fault.) So, whoever is not engaged will have a free hand to strengthen their geopolitical dominance regionally.
Personally, I think the Chinese would let the US and Russia go at it while they made very strategic moves to strengthen their political and military dominance in eastern and southeastern Asia. Taiwan, the disputed islands in the East China Sea, the South China Sea are likely targets for military action. India, Japan, Australia, and South Korea would probably dispute control of the Straits of Malacca and the Malay Archipelago. I don't think the Chinese would want the contest between the US and Russia to go nuclear because of the target list issue mentioned previously. Neither we nor the Russians are going to leave THEM around to pick up the postwar pieces either.
