If they did, and were benefiting from such an arrangement...then Russia would also be sorely tempted to sit out any escalation of tensions between the United States and China.
...and that is the scenario for the start of the Dragon's Fury Series of novels.
Horse trading - leasehold in Siberia in return for purchasing Russian commodities and mil HW.... the mother of all kick backs. Also, if PLA secure Siberia, then this solves a key logistical problem for Moscow and frees Moscow to thrust West ward and South ward with ease. Witness WW2 - Stalin was concerned that the Japanese would turn attention northward but was quite relieved at the Japanese focus on China and SE Asia, and even more relieved when Japan had to fight the US in the S. Pacific. If Russia can be assured that there will effectively be no Eastern front then Europe and the Middle East are hers.
As usual of American fiction books, you have no idea of Russian or Indian or Chinese psychi. Here is little prep: Indians dispise China because China betray close friendship pact and invade India shortly after signing...Indians still remember and arm now for revenge. China consider Russians subhumans, and so for all other peoples, and local Siberians little as animals...why local Siberians always loyal to Russia...in fear of China. Russians, and I speak from experience, are paranoid of yellow hordes, hate the east that invade us so often in past and love our Rodina like our proverbal mother...that mean every last inch of her land.
Any president who give up even portion look at likely revolution: why Yeltsin suddenly grow back bone to Clinton...generals say if Chechnya is cut free...they return to Moscow alright...straight into revolution. Why Russia and Japan still at war for 50 years, Russia retake Sahkalin and never surrender it.
Russia have trade agreements that is not even close to size of US. US is creating frankenstein by giving China everything short of own virgins...but don't worry soon Chinese will take raw resources of American women too...they are short of women. Will US give up daughters for credit to buy cheap junk too?