No issue. Official AA policy here:
http://www.aa.com/i18n/agency/Bookin...tkt_policy.jsp
Print it out and keep (to show in case a poorly trained check-in person chokes) and make sure that the connecting information you show them at check-in are the e-tickets (with e-ticket number): if they have any questions/doubts they can validate them by pulling them up on their system by their number (at the end of the day, anyone can print out a fake itinerary receipt).
And even if you already have connecting boarding passes (which you probably won't since CX will probably want to do their own passport check as opposed to rely on AA doing it), at any airline switch approach the receiving airline (at check-in, lounge, or gate) and ask them to verify that they have the connecting bag tags in their system -- you'd be amazed at how many times they don't propagate automatically! Better airlines will go looking for bags that haven't been loaded yet, but if the bag tag is not in their system they won't know that it's even missing.