And why would he do that? Why not simply play the long game whereby Russia helps facilitate altering the internal political dynamic so that (a) Estonia leaves NATO; and (b) it formerly joins a Russian centric organization.
After all, that's exactly what the US/NATO did in Ukraine, except we were impatient and had to go the direct overthrow route.
And why would/should Russia limit itself to its direct sphere of influence in E Europe? Why not use its resource base to pursue change in the Americas as well?
The problem of going into a fight unprepared for how your opponent is going to react, is that you can get your butt kicked. Trying to pull a fast one first in Syria, and then Ukraine, with our current crop of losers was a mistake from the get go.
I SAID, IF he wants the demise of NATO to be explicit. I don't know that he wants that, he may find it useful to do as you suggest.
The big deal, the only deal that really matters, is with Germany. We do not know what the Germans are thinking, and we don't know what Putin has said to their (ex-GDR) chancellor.