That's assuming the Vadwaar encountered something more than just some new expansion of the Borg all those centuries ago. Because it doesn't mesh with Q talking about the Borg existing for thousands of centuries.
There's a lot about the early portrayal of the Borg in "Q Who" that was retconned or abandoned in later episodes -- the claim that they had no interest in people, only machines; the idea that drones were incubated from birth rather than assimilated; and so forth. A TV series is a work in progress, and early depictions tend to be rough-draft interpretations that get refined and changed over time. There are a wealth of cases where we disregard the early references when later references contradict them. We accept that Data doesn't use contractions even though he used them constantly for half a season before "Datalore" suddenly claimed he didn't. We accept that Khan and his people were created by genetic engineering as stated in TWOK even though the original episode said they were created by selective breeding. We accept that Picard is an expert in archaeology even though "The Last Outpost" portrayed a Picard who knew nothing about the subject and had never heard of the ancient Tkon Empire.
Anyway, I wasn't "assuming" anything. I only said that "Dragon's Teeth" suggested
that Borg expansion was a recent phenomenon; I didn't claim it proved
it. It's one possible interpretation. Of course there are many, because this isn't real; it's just a bunch of stuff that different people made up in different stories, often contradicting each other, and the best we can do is try to pretend it fits together somehow. So of course there's no actual "right" answer.