FTstudent

Figured I'd update this, since I've returned from my trip. My routing was TPA-ORD on AA & ORD-MLE on CX, as separate tickets.
Short version: I used the Itin on the CX Mobile App to get access to the AA Flagship Lounge and to use the T3 - T5 shuttle. Once in T5 the gate agent printed our BPs, and we used the BA Lounge for the remainder of the wait.
Details: I took one of the first flights of the day to ORD to be on the safe side, leaving a long layover. Wanting to use the lounge, I went to the AA Customer Service Desk and asked them if they could print my CX BP. They said they usually can do it if the ticket has a segment on AA, so no luck. All 3 agents at the counter were discussing it, and there wasn't another PAX in line, so I took it as the best answer. But, AA agent said to show the lounge my Itinerary for access. (I was skeptical, but had nothing to lose.) Went to the Flagship Lounge showed them my CX Itin on my mobile app, and they gave us access. Seemed to take a bit of time, he kept going back and forth with the computer and my app. The AA FL is really nice. So glad we had the visit. We left the lounge around 1pm and headed to the T3-T5 shuttle. There was a big group headed down the stairs to board the shuttle, so I thought I would jump on their heels in order avoid the BP check. That didn't work. The staff stopped us. They accepted Passport and CX Itin on the mobile app as sufficient documentation without hesitation. Once we got to T5 and down to our gate, magically a CX gate agent appeared from no where. We handed over passports and she printed BPs. Never asked for Credit Card. Next we backtracked to the BA lounge and the CX agent admitted us. And then finally on to boarding.