These two abilities do Not have synergy. Am I wrong in this? Armor bane says 'when attacking', and area affect replaces attack. My friend wants to use Aun Shi's ability with gun drone units

Yes, the two work together.

Armorbane works when the unit is attacking.

In order to activate the Area Effect, you have to attack with a unit. Then, instead of choosing a defender and dealing the unit's ATK damage to it, you deal the unit's Area Effect damage to all enemy units at the planet. After that is done, the unit's attack is over. Therefore, Area Effect does happen while the unit is attacking.

Said another way, Area Effect does not replace the attack; it replaces the attack damage. There's a difference.