The idea of a connection between the Borg and Vejur originated with a joke made by Gene Roddenberry during an interview shortly after "Q Who?." He joked that the planet of living machines might be the Borg's homeworld.
I think that joke gives the theory a bit more creedence than the normal fan-theories we make here, but I have to admit, even before the internet (and so before I'd ever heard that GR had said such a thing), when I was watching TMP for the first time and the probe 'assimilated' Ilia so that she could speak for the machine intelligence, and then it mentioned a distant machine world, I totally said: "That could definitely be the Borg." so it's not a difficult connection to make.
but still not an intelligent one, no offense.
as already stated (just above) she wasn't "assimilated" it was an entirely new being that just had her look and memories...the borg are half-organic, half-machine...
again any intelligent thought shows that there's no way they can be related.
it's like saying the holodeck is borg because it can re-create "real" people. it's not even close.