Picard brought the Borg up when he was foolishly trying talk Soran out of blowing up the Veridan systems sun (Whoever thought of that for GEN needs to be retroactively horsewhipped).
Also in TNG the 'Neutral Zone' the Borg had been taking Federation and Romulan settlements. With the admission of the El-Aurians being refugees of the Borg, and in the first act of GEN during Kirk's days. We can confirm that the Borg were very much in Federation space long before the their attack on earth in TNG BOBW. If anything that attack on Earth was perpetrated because of the encounter the TNG crew had with the Borg in the Delta Quad in 'Q Who' and not because of some transmission that may or may not have reached the Borg in the Delta Quad that was sent during ENT 'Regeneration' with Archer and company. Given canon at the time of 'Q Who' airing, 'Regeneration' may have occurred in an alternate timeline as a result of the events of FC with the pollution of the timeline, deaths caused by the Borg and by the TNG crew interference with Cochram and giving him knowledge of the future.