Does the Starfinder society play any long term role in this AP? If my players don’t join how difficult does that make things?
It's no problem if they don't join. The Society is just a motivator to get them started in the early going and a potential patron down the line. If they don't join, then in book 2 the Society can still hire them to follow up on the discovery they made in book 1, seeing them as an interested and reliable outside party.
The Starfinder Society is paying them for the work they're doing from books 1-3, though once you get to book 4 they aren't really in contact. If they wanna stay freelancers, the SFS does pay for freelance work i think. The only downside is that not being licensed starfinders means that they don't carry the respect the title commands when interacting with NPCs in book 2 and 3, but if your players prefer to see themselves as mercenaries or the like that may not be an issue.
The only thing that matters is your players being willing to pursue the discovery made in the Drift Rock, and to fight the enemies that race them for it. As long as they don't give up on the plot proper, being Starfinders is just setdressing they can skip!