Do companions' skills increase as they use certain base skills?

I created a custom NPC follower/spouse at about level 25. I created her with dual wield with archery and she's currently using two ebony swords most of the time. (I have her combat AI set for archery to prefer over melee, but she still uses swords more often nowadays. It wasn't like that before.) I left her one-handed skill at the default 20 or whatever it was when I created her. I am (we are) level 40, and I've noticed as of late that she's starting to sort of shame me on fights She's one shotting and finishing people with one move on occassion. I'm like, "Man, I guess I'll just leave her alone then."

I'm wondering if their skills increase like mine do, the more they use something. My original plan on creation was to change over to melee myself, and have her for archery, since I felt that it was making things too easy for me. (I have 100 in archery and sneak.) But now I'm impressed with her dual swords too much so I'm back to archery again. If I go into the creation kit, her one-handed skill is still listed at 20, but I swear that she's kicking more butt now than ever.

I realize they can't or don't use perks (unless you actually assign them in the creation kit, which I did not.)