Yes, OLCI (and mobile check-in) works just fine. I did the same thing last month at LAX (AA to CX on separate PNRs). Checked in with the CX app and walked directly from T4 to TBIT without having to go landside.

Sometimes the CX app can't check you in for whatever reason. If that happens, just go to the CX website and check in there instead. You can then get the BP either from CX.com or through the CX app.