Russian officials have talked about doing exactly that.
Yeah, not because fucking Russians have been doing EXACTLY that every chance they have gotten since time immemorial.
Putin wants Europe to feel threatened so they will keep their weaponry close at hand instead of sending it to Ukraine.
This only works as a vague threat, but once Putin starts actually preparing to cross a NATO border, either with boots or missiles, the smart response is to push the Russian circumstances in Donbas and Crimea to past desperate. It won't do Putin much good to capture Estonia when the world is looking at 10,000 Russian POWs standing around in a barbed wire stockade. Putin's Ukraine strategy has been based on poorly considered assumptions from the start. Assuming NATO will not respond with full force and fury, including the US, would be an even more poorly considered assumption.
Even as a vague threat, it rings very hollow. The only viable asset Putin has to spare is foot soldiers. There isn't going to be an armored spearhead. The steady degradation of Russian air defenses means any troop build up along the border would become a slaughter house after the first shot is fired.
Putin is still the guy lying on the bar room floor talking about what he's going to do when he stands up.