I disagree. Finland is a full member of NATO and will host NATO forces just as the Baltics do today (they directly border Russia as well). I am no longer in the loop, but I am confident that there is already a significant ground-based signals effort operating there due to easy electronic observation of the Russian Northern Fleet (2/3's of the Russian Navy) and particularly the Boomers based on the Barents Sea. I would absolutely expect the US and other NATO members to rotate aviation and ground force units into Finland on a regular basis.
To be blunt, there is absolutely nothing Putin can do about it that would not entail national and cultural suicide.