Yes, this would work. Even if you are eligible for a card you may not be eligible for any supplementary cards, so you may only have one, in your name, which your parents could share. This depends on the card you apply for and your credit rating of course. If you have no real credit history and a bank account that never has more than a few NOK in it (sorry, I am making an assumption which could be completely wrong), you will probably not be approved by Amex but there's no real harm in applying.