I did that at check-in for CX before. I did not have the new card. So I asked the check-in agent to update my booking.

AA can be a different story. I do not know how that works. I purchased a ticket on line about three years ago. AA on-line booking did not allow me to enter my CX # (at least back then). I called them. They said they would add it. However, I still could not see my CX number and tier status when I got my BP on the outbound flight (even though the check-in agent saw my CX card and entered my CX #). On the return trip, the big EMERALD was printed. I would suggest you have some proof handy at check-in just in case.