So the repair droid has the action:

Action: Remove 1 damage from a target Vehicle unit. (Limit once per turn.)

Let's say one has a vehicle out with a damage capacity of two. If that vehicle is hit with two damage, does the repair droid have time to save it from being killed?

No, it's an "action" and not an "interrupt". The damaged vehicle is destroyed the moment it's damaged, before any action may be taken.