Will Aela the Huntress ever use werewolf form in combat?
I completed the game, and in all my time playing, and having her follow me, I have never seen her wolf out.
So, I guess not.
Normally, as said above, there is no way for her to turn werewolf...
But, if you are a PC player and don't mind a mod,
Enhanced follower Aela mod.
This may help, making her able to transform into werewolf and also the mod has some other helpful additions as well.