In the long run I find that to be doubtful. Russia has a much greater risk of effectively losing territory to China than any risk it has with the US. Much of Russia's territory is non Russian. Many territories have been pushing for greater autonomy. Han Chinese have been immigrating into Eastern Russia. The Chinese have a recent history of pursuing "historic" territorial claims. Russia has forfeited the high ground with it's actions in eastern europe.
This all adds up to a future of disputes with China. What happens when Eastern parts of Russia seek independence or want to become part of China? I think Putin is being delusional and eventually Russia looks to make friends with the west not the east.
That is a very plausible scenario. I openly admit that.
Another, and the one that worries me, is that China's ambition in southern Asia and the East and South China seas along with Russias ambitions in eastern europe and the artic leave each country looking for a way to counter balance that. It is already shown that they are starting to consider each other as a support in that area.
Some signs:
- China blocking (in addition to Russia) UN statments on Ukraine
- Russia joining Chinese naval excersizes in the South China sea
- Huge NG energy deal signed between Russia and China
- Military deals between the two for equipment and expertise
- High speed rail and other economic ties
I guess it will all come down to how hard the tension each of them faces with America and her allies (Blatic states, NATO, Japan, Philippines, Australia...). If it continues to escalate and they are pushed harder and harder I could see them deciding that it is a greater threat not to embrace each other then it is to formly ally themselves.
If those two ally formally I can think of another dozen or so countries that would clamor to join (Cuba, N. Korea, Iran, Cambodia, Belarus...)