If I put Sabine crew on a docked Attack Shuttle, I can't use her ability until the Attack Shuttle deploys, right? Because otherwise that would be terrible.

Yes. Upgrades (including Crew) on a docked ship aren't "in play" until the docked ship deploys, unless the upgrade specifically calls out an effect that it has while the ship is docked (the Phantom title).

4 hours ago, digitalbusker said:

Yes. Upgrades (including Crew) on a docked ship aren't "in play" until the docked ship deploys, unless the upgrade specifically calls out an effect that it has while the ship is docked (the Phantom title).

This is correct, even though thematically it makes no sense.

It does make a lot of sense for balance purposes though.