The Borg did not develop an interest in Earth until after they encountered Picard's Enterprise in "Q Who?," an event which was at least a century or two off in the future at the time Vejur began its trip home. And they certainly didn't develop an "obsession" until they'd had their asses kicked.
Then there's the whole issue of the people Vejur encounters. If Vejur was actually a Borg ship, wouldn't they have been assimilated? But Vejur doesn't need a crew, and the biological "carbon units" are viewed as an infestation. Vejur has no interest in them, compared with the Borg who want to "add your biological and technological distinctiveness to [their] own."
People who want to connect Vejur with the Borg would certainly agree with your interpretation, but in reality it doesn't match up at all with how the Borg actually behave on-screen.