This. The butterflies would start fluttering even before the events of The Cage, and by the time you got to the time period of TOS, there's no telling what the disposition of USS Enterprise or the TOS characters would be. There might not even have been a USS Enterprise when V'Ger shuffled in from stage left.
There was definitely an Enterprise
, as confirmed during Thelin's clandestine meeting with Arne Darvin in which the events of "The Trouble With Tribbles" were mentioned. It was Thelin who discovered the poisoned gain, which led to McCoy's discovery that Darvin was a Klingon spy as seen in the primary timeline. That still doesn't answer the question of how the V'Ger incident was dealt with, but it does confirm that the five-year mission happened despite Spock's absence.
Now, here's an interesting thought: what did Thelin do during "Journey to Babel" with the Andorian ambassador Shras Endilev aboard? I can't imagine he'd have been happy about Shras' aide trying to frame Sarek for murder. For that matter, who donated blood for the transfusion that saved Sarek's life with no Spock around? Or did Sarek not attend the Babel conference in the altered timeline? As he and Spock were still estranged in the primary timeline when the conference occurred, it's unlikely he attended because the Enterprise
was ferrying the delegates.