V'Ger and the whale probe are coming. None of the changes made will stop them, although Original Recipe Spock has knowledge that could make handling them much easier. The Borg are more complicated. It's unlikely Q will take Jean Luc Picard and his Ent D to the Delta Quadrant since Picard probably won't exist anymore. If that doesn't happen, then the Borg won't move towards the alpha quadrant anytime soon.
The Borg are probably on their way - remember, they still will eventually (in the 24th century) receive the signal sent by the Arctic drones in the mid-22nd century. Unless another Alpha or Beta Quadrant ship gets sent their way, they may not take as much an interest as quickly as before, but they will still make their way toward Earth.
Changes to the timeline would propagate into the past if they alter a backwards time travel event. In other words, if the time travel in First Contact is prevented then there would not be any Arctic Drones to send a signal.
No....
They created a new universe when Nero and Spock altered the time-line, but everything that happened to their universe before the intrusion was identical, including the crash landing of the Borg sphere in the Arctic. As Spock was able to travel to the past and stay in the new time line without being "erased", so too would the downed Borg. There would be no "time wave" or whatever altering past events.