I don't think there's such a strong support of Wagner in this case for that to happen, though, from what I'm seeing in TG channels everyone are treating them as traitors and I doubt the feeling in the ranks is much different, maybe there are some loose ends where money is involved but otherwise it would be very unpatriotic to support Wagner.

they were able to sweep the Whites aside with relative ease.

In Petersburg at first yeah. But the civil war was incredibly hard. If whites actually managed to coordinate even with themselves, not to mention with intervents, they would probably won. Hell, the worst moment in war was when Yudenich managed to somewhat coordinate with Kolchak, and even then Kolchak fucked it up by being stuck up imperialist pig.