Oh, my yes. That is the (literal) trillion (and more) dollar question alive in the world right now.
My guess (though I repeat your BWDIK) is that the US military would adapt less quickly than the Ukrainians (if only because it's got a lot more doctrinal inertia), but more rapidly than the Russians did. There is a sub-genre of military history dedicated to figuring out how/why democracies - going back to antiquity - tend to punch above their military weight. The suppositions tend to cluster around 1.) they don't fight unless it's truly popular, which unlocks a comparative man-power advantage, and 2.) an egalitarian social / political structure makes distributed authority and acceptance of new ideas more possible / palative.
Unfortunately, the Russians have now adapted to drone warfare (even if they haven't matched the innovative pace of the Ukrainians), and I think Western Europe should be more scared of their military than they were two years ago. That's my cold hard-eyed real politiik case for supporting Ukraine: the West needs the world experts on this new military paradigm on-side. Perhaps the primary challenge this argument faces (particularly in the US - the Europeans don't all share this psychology) is a reluctance to admit (in culture or military doctrine) that "we" aren't The Best at something. The notion that OCS could be materially improved by importing any random captain from the Ukrainian front to teach a few classes is a tough one to swallow.
Disclaimer: I'm not military, only an observer through media, and through conversations with current and ex-military friends. Several of those military friends have become, in the past few years, super interested in flying drones in their spare time. They're already preparing to adapt, even if their commands are moving more slowly.