If you have an itinerary I would suspect you can get through the T4-T4S security and into the lounge, where the Iberia folks should be able to call down to the AA gate and get your pass waiting for you at the gate.
i did the revese last week — AA to ORD then IB to MAD and onward. AA would *not* through check and gave me some hooey about liability and tracking.
But the AAngels at the Admirals Club and the FL said that terminal transfers were permitted without a boarding pass at ORD—just an itinerary (printed) was required since they couldn’t access IB systems.
i couldn’t check in for my IB flight and I just went down there at boarding and they checked me in and got me a boarding pass.
i suspect your only problem will be clearing security and exit Schengen immigration — and I would suspect that a same-day-itinerary will suffice.
A wild card would be if at your point of IB departure there are SABRE ground agents working some other AA flight that might be able to get your AA pass (I’m thinking something like if you are at CDG and could get to the Admirals Club and have them print your pass and do the security grilling).