Sure. Russia and China are natural enemies as they are both Eusasian expansionist empires. The only thing that stops this is the fear/respect they have of each other and more importantly, pursuing common interests such as undermining common enemies. The end of the cold war was the perfect time to bring them over to the side of the west. Russia was broke and desperate, China still didn't have their shit together, and the west was sitting pretty on top of the world.
Instead though the goal has been NATO expansionism, and undermining Russia's regional influence. For a full sequence of events check out the presentations of Vladimir Pozner, he is a French/Russian/American journalist and former diplomat. He has covered the subject extensively. The result is that circa 2050 when the new cold war happens between America and China, Russia will hate us and support China at every step.