I believe the smallest change can ripple through time like a snowball.
In reality, it probably would (if time travel is possible in the first place, and we aren't stuck with the complete lack of any possibility for such change, that is).
In Star Trek, clearly not. We have seen many time-tampering stories, including ones where live after time travel is significantly different from life before time travel, yet none of this seems to erase either the time-traveling heroes or their non-time-traveling contemporaries and loved ones from existence.
Whether this is just predestination (every time travel adventure was always supposed to happen, and only one valid timeline exists) or a case of time repairing itself or being repaired by detail-minded caretakers of some sort, we don't know. But it does seem to follow that one doesn't accidentally prevent WWIII if one sets out to prevent toothpicks from getting invented, or vice versa.