I can buy that the Hansens were chasing half-baked rumors of a dangerous and powerful interstellar entity of some kind in that part of the galaxy (rumors from the recalcitrant El-Aurians, who obviously would not have wanted their rescuers to go tweak the Borg, or from Cochrane's drunken rantings), went out further than anyone in efforts to investigate those rumors, and found a lot more than they bargained for. Obviously, they never got a chance to report back in on what they found.
While the continuity is somewhat stitched together, it still holds up okay. The real first contact between representatives of the civilizations in which someone survives to tell the tale and actually has a name to put to the threat is still "Q Who?" If Q had not zapped the Enterprise away from the Borg at the end of that episode, they'd have merely disappeared as well, with the Federation no wiser about the Borg despite the loss of several outposts and colonies along the Romulan Neutral Zone to their hostile action. It's difficult to gather and disseminate reliable intelligence on an enemy that tends to overwhelm all resistance so quickly.
I just didn't like the suggestion in "Regeneration" that the Borg would be coming because of the signal. Of how much interest could Earth and its minor space program be to the Borg most of the way across the galaxy? I always thought that the Borg just happened into the Neutral Zone area and continued on their way, not judging either the Federation or Romulans worthy of further time, until the "Q Who?" incident in which they saw Enterprise-D display capabilities they did not understand. Of course, we the viewers know it was Q, but how could the Borg know this?
I believe that after that incident, the very same ship headed straight for the Federation to find out what was what. I don't know why the Queen then decided to play games with assimilating Picard and naming him and wanting to marry him or whatever that B.S. was; maybe it was because the Federation didn't turn out to be the power she expected, but she picked up on the connection between Picard and Q in computer records or something like that and was curious to see how much more she could get going. Perhaps all her weird efforts could be rationalized as attempts to get Q's attention with unpredictable methodology and personal connections to Picard. She may also have only gone back in time to fulfill the predestination paradox of the signal being sent in "Regeneration"--hey, she probably knows more about this crap than we do. Ted, don't forget to wind your watch!
Either way, it seems pretty clear that the Borg aren't exactly dedicating all available resources to assimilating Federation worlds; indeed, why should they? It can't be THAT great of a prize compared to other powers nearer to their point of origin. I'm sure they have better things to do.