I liked "Regeneration" as a Borg episode even if it made a bad Enterprise episode, but yes it messed up the Star Trek timeline even further than already in Voyager when it was revealed that the Hansens were studying the Borg, or in Generations when it was revealed that the refugees were El Aurians or included them among other species.
Knowledge about a 'lost' or 'mystery' species would be recorded, especially when some sightings have similarities (mysterious cyborg aliens, you don't ignore that quickly).
If the El-Aurians on purpose did not tell the Federation about the Borg Collective it rather speaks a lot about the El-Aurians' mentality (we should not warn the Federation about this civilization of cyborgs that will probably come for it and its people when the Collective realizes that it has technology and resources the Collective can use, the Federation must meet the Borg on its own).
Even Hansen's crackpot theory about some mysterious species traveling through space in large cube shaped vessels would probably end up in some archive, even if it is just some silly idea that can not be confirmed nor denied.
The moment Picard and the Ent-D crew ran into a Borg ship and came back to tell the tale should have might some lights go on (cyborgs? cube shaped vessel? Wasn't there some crackpot scholar who had this theory about a 'Borg Collective', some mystery species that has only been seen at the edges of explored space?)
Section 31 covering it all up? Forcing the El-Aurian refugees to remain quiet for example, why would they?
If anything they would encourage research and investigation into this unknown species as it could clearly be some kind of threat. They would want more information about this species in order to have counter strategies and new weapons be developed for the inevitable day that the Collective would show up.
They would probably hire Hansen through a third party to investigate the Collective, or perhaps even send probes way back on the 22th century in the rough direction of the Delta Quadrant once Archer had send his report of the events of "Regeneration".
No, I honestly think there should not have been a Borg episode in Enterprise (or the Enterprise series to begin with but that is another subject) or any references to the Federation knowing about the Borg Collective before "Q who". (the idea that Guinan and other El-Aurians knew about the Borg but never told anyone is a whole different can of worms)
Perhaps Seven of Nine should have been a Starfleet member or Federation civilian who got assimilated by the Borg after "The best of both worlds."