And there is also the possibility of non-destructive convergence, i.e., what happens when an altered timeline is "patched," and the actions of those "patching" it are incorporated back into the unaltered path (postulated, as I recall, at the end of Assignment: Earth, either in the actual script or in Blish's adaptation).
The idea in A:E was that, as Spock said, "It appears we did not interfere. The Enterprise
was part of what was supposed to happen on this day in 1968." I.e. it was a self-consistent time loop, the time travel being necessary to cause the events that led to the travellers' established history in the first place. As with Spock's kahs-wan
, if they hadn't gone back in time, that
would've altered history. (Albeit only slightly, since Gary would then have been able to carry out his mission with no interference and the missile would've just blown up at higher altitude.)
That said, I did postulate in WTC that if a timeline were changed only slightly, just a minor perturbation that had no lasting impact on events -- like, say, O'Brien and Bashir being chewed out by Kirk after the bar fight on Station K-7 rather than the two other guys who were originally standing there -- then the resultant altered timeline spontaneously merges back with the main one, because the differences are too trivial to cause a divergence.