Imho, you could indeed adopt the bacterium from the parrot. That's something totally different from allowing it to colonize, let alone infect, actually. S. pneumoniae is part of the commensal flora in your nasopharynx and causes no harm in most cases, though is a professional invader and one of the three most important causes of airway infections (this one and H. influenzae are also quite infamous for meningitis), along with Moraxella catarrhalis and Haemophilus influenzae (infernal trio)... But as long as there's no opportunity for them to really infect you, there's no opportunity to get sick from them so ... infection from a parrot? No, unles you give it good conditions to.
Oh and btw, the pneumococcus is transmissioned by droplets, so unless you actively collect parrot saliva or snot (do parrots sneeze?), don't worry.