I'm not sure if they previously did, but I called them to find out if they do that now and the response was no, they only grade either the auto or card. The rep didn't have a reason, and it seemed like she thought there would be no good reason for not being able to grade both.
I'm pretty sure they did, but have no idea when they stopped. I'd contemplated sending a few of my mintier signed cards, many years ago, but never did.

Isn't this a graded auto card?