If a defender with Imperv rolls a 5/6 Vs an attack with Armor Piercing, does the defender still take 1 damage?

Yes. AP says that the damage dealt by this character can not be reduced below one. If you roll a 5/6 it reduces damage to 0, but during an AP attack, that can't happen.

That is the whole point of AP to go through Imp. and Inv. especially for characters that do only 1 Damage. (Think Silver age Flash)

poison!+ap.