I am suggesting that they could initiate and support an insurgency.
Again, insurgency will be supressed by regular army. Chechnia was "war against terrorism" in the land there living population itself supported terrorism. This is not possible in Siberia.
Just image this scenario between Mexico and USA in Texas. Is it possible? You say about something similar.
Unless you are saying the US did not support the Chechens?
USA didn't do it at least directly. Something like "some organisations in middle-east, which were supported by USA support Chechen's uprising - maybe, and yes. There were nor direct "help" nor claims to free Chechnia through UN.
But there was informational war in plain of "evil russian supress freedom fighters" - some sort of yes...