Here's my take on this question, my answer is yes or no. It all depends on your credit profile/s, Do you already have a few CC's? Do you have a decent AAoA already?
If you have a decent AAoA already with a few CC's, adding a "New CC" will lower your AAoA, potentially lowering your AAoA to a point 1 year younger which could hurt your score, it may not, YMMV (Fico rounds down AAoA) Not to mention the inquiry, that could lower your score, again YMMV. The inquiry will only affect the applicant not the AU (like stanggt03 said you will need a CCC that allows AU's and also will report to the AU's reports)
It could help your score if you have no revolving credit at all, You may not see dramatic score rise, but you could see a bump, going from no revolving credit (100% util) to having a CC now listed on your reports would bring down your util with its CL, so it could help you, but you have to keep your util <9% to see your best scores. Just in case you don't know util is, your debt to avail revolving credit.
There is so much more info we would need to know about your credit reports to be able to tell you for sure if opening one CC will help you and the other person. Your post is very vague, making it very hard to give you a reasonable answer.
EDIT: re-reading your post and your subject line, two different questions. I gave my 0.02 cents on your subject line question, but to answer the question in your post, you would need to call the CCC that you may want to apply for and ask the CSR if they allow AU's and if they do, do they also report the TL on the AU's reports, thats what I would do before apping for just any card.
