^Nope. TNG never states exactly where the Borg come from; it's left very vague. The closest it comes is in Q Who, the Borg's first appearance, when they encounter a Cube in System J-25, which is only stated to be 7,000 light-years from Federation space. The Delta Quadrant is never mentioned in relation to the Borg. In fact, the whole concept of dividing the galaxy into four quadrants wasn't even introduced for another season. I'm of the opinion, and it is just my opinion, that the reference to the Borg's Delta Quadrant origins was inserted into First Contact (co-written, I think not coincidentally, by Brannon Braga) in order to pave the way for their introduction on VOY, which came just a few months after First Contact premiered.