An update:

I tried to get boarding passes for all legs in OPO, but was told this was not possible. Iberia only gave me a boarding pass for the 1st leg to MAD, told me to get passes at the transfer desk in MAD in the same terminal (4S). They were able to check my luggage in to ORD, but not to the final destination (I was connecting at ORD to another US city). So I was to collect my luggage and recheck it in at ORD. I was not sure this was possible (I had only 1hr 45min at ORD), but that was what I was told.

I got to MAD terminal 4S, 10 min late, and there was NO transfer desk. I was told by security to go to terminal 4, so of course I missed the flight. Iberia then rerouted me via LHR, by BA, and send my luggage to the proper final destination. I was not given an explanation on why I could not be given boarding passes in OPO.
There were a couple of empty seats in MAD -> LHR, and LHR->onwards was only half full. In the end, I was only 1hr30min late at the final destination than the original itin.