Assuming the real deal here is kid who can't get card on own is pushing for mom to get card so kid can use miles @:-)-- yep, it can work, but, keep in mind that the big miles benefit is in the bonus miles (say 50K on AA Citi card--be sure to read thread on AA Citi deals) and most of those bonus deals these days require a minimum spend of $3-10K or so within around three months.

And, as mentioned above, miles will go to mom, not kid, even if authorized user. However, mom can use her miles to get a ticket for kid--would be nice to take mom along!