NATO is an organization, not a country. So, Putin may invade a NATO member but unless he's managed to infiltrate a lot of FSB operatives into NATO HQ, he can't invade NATO itself. And let's face it: why would he bother? NATO is a hollow shell, an empty joke. The creature Trump has made it clear the USA under Republican rule no longer regards NATO as an obligation. The dithering imbecile Biden is too spineless to react even if by a miracle he clings onto power in the November election. No European NATO member has any meaningful capacity for self-defence. Thus, Putin will almost certainly take the Baltic states and put pressure on other NATO members to capitulate (Germany will crumble almost instantly and will eagerly pay "reparations" to Russia in order to enable Putin to re-arm more quickly than he otherwise could). Most NATO members will shuffle off into the shadows, Finland will return to its previous posture of pseudo-independence, and all eyes will turn to Asia as China first takes Taiwan and then begins to consider the advantages of owning the Philippines. But Putin won't ever invade NATO because you can't invade a dead abstraction.