Too many variables to say for sure, even if the overall story remains the same.
Is Tuvix a stable combination? Will he start assimilating other crewmembers into the gestalt if he's transported again, seeing as that orchid is still part of him, as are the fusion proteins that caused Tuvok and Neelix to merge in the first place. Or is he vulnerable to something that would not affect them separately, due to his unique hybrid nature?
Will Tuvix suffer from the same neurological issues that make Admiral Janeway resolve to return to the past, and get Voyager back home to Earth before his condition causes irreparable damage? Does Voyager maintain the same decisions in those off-screen decades to cause the same thing?
Tuvix himself also has agency, an emergent individual who is both and neither a fusion between the two. Would he make the same decisions in those same circumstances? We don't know. Maybe Tuvix might not leave the Voyager shortly before they go home, or maybe he might decide to forge his own path separate from what Tuvok and Neelix might have done.
The only thing that we can really say for sure is "maybe"? Assuming that the rest of the story is close enough to have the events not wildly deviate, then Tuvix would act like the two, close enough that the sequence of events is maintained, and there are no major consequences for their fusion, except an open question on whether or not it can be undone.
Maybe the fusion is what caused his neurological condition, and the same motivations for Admiral Janeway would apply, with the taking the chance to save Tuvix (instead of Tuvok), ultimately leading to no major changes in the timeline. Most of it would remain the same. Whether his marriage with his wife would remain is another question entirely, seeing as Tuvix is technically a completely different entity.