I managed to to speak with a live EI employee at Cork airport.(as opposed to phone agent who never seem to give a definitive answer) She assured me that they would be the ones printing my BA boarding pass and forwarding my bags to the BA flight. She also said the there would be no problem if I wanted to select/change seat assignment on my BA flight. She even went so far as to give me her name and mobile number, just in case. When I mentioned I was arriving in Ireland on another airline, she told me to bring a jacket because apparently it's chilly over there. (it's 97 degrees in the US right now)