I think there’s an outside chance that once in-theater, these Chechens would turn on the Russians and join the Ukrainians.
More the Russians turning on the Chechens and then Putin for allying himself with Muslims against fellow Orthodox Christians. After years of restoring the church among the Russian people this would be seen as the deepest betrayal. An "Operation Valkyrie" can't be ruled out.
No they won’t, these are all soldiers of Chechnya’s regular standing paramilitary. They’re not yahoos being scooped up and given guns. They have been deployed combat in the behalf of Russia for over a decade.