I've had nothing but fun with my Varanus FSV; I've got it speced where it can survive against Borg ships. I have seen the repair drones repairing my ship during and after battle; the hull has to drop to 85-90% before they activate. The biggest problem is that they have the hull strength of your average shuttlecraft, so if the enemy targets them, they don't last very long, and you can't repair them. Best suggestion is to use the Scorpion fighters as an attempt to draw enemy fire from your drones.
Of course, I also have an Engineering character commanding the ship, which probably helps.
What boff abilities did you go for, especially the science based ones?