To be sure, "Immunity Syndrome" only establishes the Intrepid as a "starship" that has stopped answering hails, not as a Starfleet or Federation vessel, or one that would do Starfleet's bidding. While few other vessels in TOS are called "starship", and all of those are associated with the Federation somehow, the other shows tend to use the term "starship" for foreign vessels as well. And ENT uses it that way, too, establishing a "precedent"...
So if the movie goes the unlikely route of insisting that Spock was the first to enroll, graduate, and rise to Commander rank, the Intrepid can in theory be ignored here.
Timo Saloniemi