I'm an AMEX member since 2010.
My brother is an AMEX member since 30 years ago.
If my brother adds me as AU onto his account, will AMEX backdate my card 30 years?
First, Amex has additional cardmembers, not authorized users. This is an important distinction, because authorized users usually get the entire history of the card added to their report, whereas additional cardmembers will show up like a new account.
Second, probably not. I know that Amex used to give additional cardmembers the member since date of the original cardmember. They officially stopped doing it in 2011 and I haven't seen someone report a success through that method in at least a year.
If you are lucky, the card/account will show "member since" date of 2010 (your original), but be warned: it may show 'member since" 2012. This is what happened to my wife. She is an amex member since 1992. I added her to my hilton card. It said "member since 2012" and reports to the CRAs as such. We have tried repeatedly to get this changed to 1992 (not even 1988, my member since date) and have been repeatedly rejected. It may eventually happen (we call every month), but it may not. So be prepared for the potential that doing this could, in fact, reduce your AAoA.
Of course, you could get lucky. For every Amex rule there is at least one post from someone swearing they got an exception. So you might. But you should only do it if you are prepared for the alternate consequences. In general, adding AU to help with AAoA is better done with visa/mc than with amex.