I suspect it would be more than just a distraction for him seeing how he needs all hands on deck in Ukraine, but even just a distraction would be disastrous for Putin. The only reason he might want Belarus fighting with him is to keep some Ukrainian forces tied up and away from the main theater in donbas.. I mean even Putin isn't stupid enough to think Belarus could hope to occupy Kyiv.

So if it backfires, and he ends up being the one needing to divert troops to quell a popular uprising in Belarus he would've found yet another way to screw himself.