Surely if anyone would know for sure, it'd be the 30th century time cops who scan time as easily as the 24th century Trekkers scan space. And they called it a "pogo paradox", where interference to prevent an event is what causes it.
It's always a bitch to try and reconcile 45 years of Treks, with generations of writers and producers all with their own idea of how the Trekverse is meant to work. First Contacy and the Enterprise TV series are huge retcons, but I'm more than willing to go with it and pretend Trek's history "always happened" like that. Even if the subject of the NX-01 never once came up in TOS, TNG, DS9 and VOY, except for those extra scenes in "The Pegasus" where Riker and Troi suddenly look a lot older.