I'm not sure how you would get to that situation, but a 0* attack that resolves to 0 would add any bonus damage. So a 0* that rolled and got 0 damage, would add 1 and be 1 total damage.
A straight 0 (not 0*) would not add any bonus damage. We've tried to list 0's as -'s to be clear that a 0 damage rating is no attack at that range, but I'm sure we missed some. You need at least a 0* to attack at that range, even if you've got something that adds damage at that range. So if you have AC 2/2/0 and OVL wit OV1, you can't add the OV1 to an AC special attack that only uses AC damage values. If it was AC2/2/0* with OVL and OV1, you could add OV1 to the AC damage at long range.