When are those 2 damage dealt? Before or after the additional action? This may be relevant, if your Droid is down to 1 or 2 health.

I read it as if you have to suffer the damage first to be able to spend the extra action. But this is my personal interpretation

During a Droid's activation (i.e. when not performing an action), the Droid can suffer 2 damage. If the Droid suffers the 2 damage, that droid may perform an additional action during that activation.

If the figure is defeated by suffering the damage, the activation immediately ends, and thus the figure cannot perform the additional action.

No Overdrive for my Junk Droid ...