Good question. I was an authorized user on my Parent's credit card when I was young before I got my own and I don't think it helped. Either that, or 1 AU wasn't enough to get me enough history for my own credit card.
It is not the card number, it is her SSN you gave when adding her that identifies her and gives her the report.
If you look at the back of your Discover card, under the Disco, Diners and Pulse logos, there's a card identifier that starts with "A". (A001, A002, A003, ~) This is how Discover knows which card is being used. You can have multiple card designs in hand and turn them off/on online using these identifiers as well.
As eastsea said, Discover will report her as an AU using the info you provided for her to get a card on your account.