Possibly! One reason why CX boarding passes don't print is that for various reasons they want to check your paperwork sooner than at the gate when boarding. So have you entered all your passport and nationality details in CX's side of MMB, for example? I don't think your assistance request from T5 to T3 will have anything to do with it.

Now even if you can't print out your boarding card, it is VERY important that you print out the itinerary details, assuming this is not a code share. The reason being that you will presumably be transiting from T5 Domestic, and at the glass door that gets you to flight connections for T3 the staff there are required to see either a boarding pass or some other travel documentation to prove you need to be airside, so you best have this to hand after you leave the ABZ flight. You do not go to T5 Flight Connections. That itinerary, with the CX locator, will also be used by BA in ABZ for checking in luggage. It would also be helpful if you had the ticket number visible too, sometimes the CX PNRs confuse agents.