The FAQ is clear that Saar Space Docks are not ships, cannot retreat, and are not affected by High Alert. On the other hand, it says Saar Space Docks CAN use Antimass Deflectors and Maneuvering Jets. So does Gravity Drive work for Saar Space Docks or not?

The answer would be: No.

Gravity drive specifies ships, and the saar space dock is not a ship.

The tech implies that the mobility of units exiting a Gravity Rift tile are increased by one… as the Saar Space Dock is a part of your armada I would rule in favor of it gaining the same ability…

As "Gravity Drive" clearly specifies that Ships gains +1 movement and not units; i would say that it didn't apply to Saar space docks.

"Antimass Deflectors" and "Maneuvering Jets" are both explicitly referring to ships, regarding the ability to pass through Asteroid Fields/Ion Storms.

But Saar Space Docks are affected by these Technologies still.

Following this canon, "Gravitiy Drive" would at the very least have to let Saar Space Docks pass through Gravity Rifts safely.

Saar Space Docks are immune to most harmful effects (PDS, Mines), and can cancel more negative effects through these drive-technologies.

Then, all movement boosts from blue Technologies always mention specific ship-types.

Except for "Gravity Drive".

Personally:

Since, theoretically, this type of movement does not use specific new propulsion engines, but (I guess), some type of swing-by-/gravity-surf-principle, it should be applicable to all units you are able to move through Space individually.