If Russia were to attack NATO, they would do it in the Baltics. Russia, and Vladmir Putin covets them.
The Baltics are the only part of NATO that shares a land border with Russia (Kalingrad aside). The borderlands have Russian speaking populations, many descended from those that were transpanted there during Soviet times.
The most likely action for Russia in an attempt to seize the Baltics (or seize a large part of them) is to claim that the governments are engaging in some kind of anti-ethnic Russian activity, and that the locals are taking up arms to fight the tyranny of the Baltics government. Those armed locals, of course, would be these Russian mercenaries, or Crimea style "Little Green Men".
Once Latvian, Estonian and Lithianian security forces move to confront the these armed Russian interloopers, Russia would send in it's conventional forces to "defend ethnic Russians in a humanitarian intervention", and then dare the US to evict it.
The above, broadly, is the most common outline for how Russia invades NATO territory. The mercenaries give Russia plausible deniability, predating the sending in of conventional forces as relief. This is exactly what happened in Ukraine. And the reason is the same. Russia was concerned about Ukraine joining the EU one day, along with NATO. This would give NATO ground forces a quick and easy drive right into Russia's soft underbelly. Seizing the borderlands gives Russia a buffer. It would be, conceptually, the same thing in the Baltics. Russia would have a borderland under control of "the locals", which would really be Russian mercenaries, as a buffer against a NATO ground force.
Is it stupid? Yes. It is completely stupid. Russia is so historically obsessed with preventing the next Napoleon or Hitler from marching on Moscow, they've long under-prepared for the fact that NATO would never, ever strike them like that. I mean, really... sending NATO tanks INTO Russia? It's a completely crazy idea. If push came to shove, the US would do many, many things to creatively bludgeon Russia, but never that. They should be much more afraid of long range bombers from the Middle East and Indian ocean.
But hey, Russia's afraid of what its afraid of.