Not. The two have been allies to some extent for a long time, and while it's not all "about us" a good part of it dates to the '90s when Russia and China both saw Yugoslavija bombed. Russia saw it's Orthodox Serb allies targeted, and let's not forget the wonderful outpouring of Chinese nationalistic enthusiasm when we hit the Chinese embassy in Beograd.
It is about a balance of power, dating to when China was weaker.
But it's also about shared borders and resources and, well, tactical and strategic goals. Russia has a huge sparsely populated, resource-rich area. And it went ballistic when it was implied that it's too large a country, given its population and resources. That, next to a very well-populated, resource-hungry country.
And let's not forget that while the US/Mexico border is "poorly defended," the Chinese/Russian border isn't probably even demarcated for most of its territory. It would be very, very easy for Chinese to make up the overwhelming majority of the population along the most useful strip of territory in that part of Siberia, the bit along the Chinese border. Then for the Chinese to develop a historical claim that it was once, at least for a day, part of Greater China--and once part of China, always part of the Chinese Empire. Uh ... part of China.
While Americans may forget that China's been involved in a few military skirmishes, Russia doesn't. So it made sense for a markedly weaker Russia to cozy up to a China that was paranoid about the US, in geostrategic terms.