No, the assumption is that you must be 18 years old to apply for a credit card. Surely we could have the machines determine that an "authorized user card" does not guarantee 18+ but the actual card does.
ceejayoz> You want to let every merchant I swipe my card at know my age? To improve privacy?
Remember the site guidelines:
SG> Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize.
The obvious solution is instead of "every transaction comes with the user's birthday", the vendor can in some way set a minimum age enum of say (13, 15, 18, 21, 25) — a handful of ages that are significant with respect to some law or regulation. Then the transaction succeeds or fails.