The same is true for any other partner bookings that don't involve AA. I've done several trips all on BA (AUS-LHR-DEL), CX (ORD-HKG-CMB), etc., and none showed up on the AA app.
I personally use TripIt, and have for a long time (over 10 years), and it works for me to keep all of my travel stuff in one place (air, hotel, car, etc.) But like I said upthread, there are several similar (perhaps better) tools out there.

Actually TripIt downloads the itinerary to the device, and saved me when I wanted to enter the DEL airport. I didn't realize I'd need to show an itinerary just to get inside (the one trip when I didn't print out everything), but I was able to show the guard my BA DEL-LHR flight on the TripIt app and he let me enter the airport building.