There's plenty of alternative communications systems in place and I presume the military does not depend exclusively on one, two, or even three systems, least of all the relatively vulnerable internet cables. NATO, borders, and the Russian invasion response playbooks predate the internet by decades, too.

While theoretically it's possible that Russia would simultaneously dismantle or jam the internet, mobile phones, radio, sattelite, and runners in fast cars, if that does happen it's already red alert everywhere.