Nobody who has been paying attention would classify China and Russia as allies. China didn't support Russian annexation of Crimea at UN and Russia supplies India with vast quantities of weapons. Their only cooperation is through their collective hatred of the West. When Putin dies, it's likely the next guy will be a full Westphile and work with US to contain China. By then, though, China will be too big to contain even with Russia against them.
This isn't an unreasonable line of thought, however it mistakenly implies Putin's successor will attempt a pivot back to the west. Note the primary issue of difference is the baltics, ukraine, and crimea. These are places with heavy native russian population and which have been at some point in history part of "russian lands". While there may be reasonable accommodation in Baltics, I don't see a russian leader surviving by giving up Crimea or allowing re-integration of the donbass into Ukraine. Furthermore, another front has opened up with Belarus, which also has extremely close language, ethnic, and cultural ties to russia and now also subject to western sanctions.
The issue isn't that Russia is willing to improve relations with the west, but rather the key issues of difference are non-negotiable. A "democratic" Russia wouldn't have materially different positions on either ukraine and crimea. Maybe they wouldn't have invaded to begin with, but they would never give it back, the people who live there are now considered fellow russians, and you dont give up your countrymen unless you are defeated in war.
At most, Russia will be a neutral player in China vs US (and even then, that should already be considered a US victory). Europe's security concern is still with Russia, and if US got too cozy with Russia, EU would continue building out "strategic autonomy". Keep in mind that china's leverage against Russia is also that it could simply re-engage with central Europe in a way that its not doing right now. If Russia were to go against China, China could easily start pressuring Ukraine and Central Asia. These are not traditional Chinese areas of influence, so it would be a struggle for russia to lose. A US thaw on russia could also be seen as betrayal of eastern europe. While europe still relies on Russia as a source of hydrocarbons, this dependence will only last another 20 years as they persue alternative energy. In that respect, Russia's strategic leverage against Europe is decreasing.