Would I take friendly fire damage if I had a mage as companion?

I'm playing Skyrim as a battle mage. Thus I focus on heavy armor, desctruction magic and one-handed.

At the moment my companion is Lydia. She always runs in the line of fire and tells me to stop hurting her. I also managed to kill her many times using chain lightning or fire ball.

Thats why it came to my mind using a ranged companion.

If I had a destruction magic companion would he also do damage to me when he casts an AOE spell?

Yes.

Source: Personal experience with Illia as a follower (who likes casting the AoE frost spell, Ice Storm).

Also, this UESP article about Illia seems to back me up:

Illia favors Frost spells. This can be particularly devastating in combat to both enemies and the player, as she frequently uses slow moving AoE Frost spells after about level 20. Players specializing in melee should be particularly careful with her as a follower.

I recommend using measures to increase magic resistance or resistance to the element of the spell that your follower favors using.

List of followers here: http://uesp.net/wiki/Skyrim:Followers

Check out which ones use which types of spells. Note that non-mage followers, that are given staves that cast AoE spells might use them and hurt you too.

You might also want to consider an archer-type ranged follower (Faendal, Aela, etc.), instead. They seem to take extra care not to hit you, unlike their AOE-spell using mage counterparts.