City on the Edge, Past Tense, and First Contact all suggest strongly otherwise.
I must respectfully disagree:
- City: How can we be absolutely sure that McCoy wasn't "always" supposed to travel back in time?
- Past Tense: Sure, at the end of the episode, Gabriel Bell looks like Sisko in the computer records. But nobody bothered to look this up before they went back to 2024, did they? Who's to say that a search wouldn't have turned up Sisko's face then, too?
- First Contact: The Enterprise returned to the same future it left. And we have no proof that Cochrane's original crewmates on the Phoenix were ever anyone other than Riker and Geordi.