I don't know if NATO would, but I know Ukraine would. Best way to end the war is to let the side that refuses to consider peace know the price of continuing. If Russian cities where getting wrecked like Ukrainian cities, would Russia really still want to continue? If their infrastructure was destroyed, could they continue even if they wanted to?

I am also rather certain that some nations in NATO would invade on their own even if NATO didn't. Russia is now weak and their military is in shambles, but they keep provoking western nations and they still have tons of valuable resources... normally this would mean Freedom ^TM for them, but they have nukes.