From reading the descriptions of each of the types of armor piercing ammunition in RAGE, it looks like using armor piercing ammo on a non-armored target will do less damage, as a portion of the damage the ammunition does is to pierce the targets armor.
As per the ammunition page there are quite a few different ammunitions that have an armor piercing ability. Here is some reading;
Feltrite AR Rounds: The structural strength provided by Feltrite allows higher penetration and cause more damage to armored targets.
Authoritiy AV2x Rounds: ...being able to put down both the unarmored and armored enemies quickly. It is much more useful against the heavily armored enemies such as Gearheads and the Authority infantrymen.
Steel-tipped Bolts: The bolts deal considerable amount of damage to the enemies. This ammo is effective against all types of enemies, as even the strong and armored enemies such as the Authority troops or Gearheads...
My conclusion from this is that armor piercing ammunition is still useful against unarmored targets, but gains additional damage in the form of piercing armor against the tougher enemies that do have armor.