Oh, she'll wear whatever armour you give her as long as it is better than what she's currently wearing.
I'm level 20 now and I've never used a scroll in a fight or a Shout outside of the training bit with the Greybeards.
I'd probably have to mix it up if I didn't have Lydia with me though. Does giving Lydia (or any other companion) armour and weapons actually have an effect? I've noticed that the game doesn't take into account enchantments when saying which weapon is better so, for example, I gave Lydia the Wabberjack to hold and that became her default ranged weapon instead of her bow. When I put that together with the fact that I can't choose what armour she wears or what weapons she's using (unless I've missed it), it makes me wonder if giving her fancy armour and weapons actually does anything.