This just isn't China's style. China has a steady policy of noninterference in a sovereign country's internal affair. They see things like arming insurgent groups as the kind of thing American and Western powers do and have an aversion to doing the same thing. If China really wanted to put pressure on India, they have far more direct and pointed methods.
They can start building more airbases in Tibet and shift more of the Western Theater air brigades from Xinjiang to there, they can increase the border garrisons, they can beef up infrastructure on the Indian border, they can increase the frequency and intensity of air patrols, and so on. The best thing about all of this is that it forces India to respond in kind, and they're not in a good position to do so, so it'll take a lot of pressure off the Pakistan border.
