SSR handles the space side. If AA has a problem with the SSR the can bounce back the message. If the SSR is accepted then you are OK on that side at BRU in terms of space. So when the bag enters the system at BRU then you're going to be OK in practical terms. Ideally when you get Iberia to submit the SSR they will email you a screenshot of it or some other confirmation but that will probably be wishful thinking. You can turn up without the SSR but then you have a risk of being turned down or moved to another flight to accommodate the bike.

Bike boxes tend to weight 10 to 12 kgs if rigid, or as little as 3kgs if cardboard, but the latter is clearly insufficient to protect the bike.