Everyone thinks Morgan awoke due to her getting involved with Dodger and his intrusion; I'm here to tell you that that just ain't so. The precise instant of her deviating from her 'set path', i.e. her code, comes when both Dodger and Twist are intruding on her v-space - and though I haven't read 'Never Deal With A Dragon' in a while (the book in which Morgan is awoken), I can't swear absolutely to Dodger's presence at that specific point.
Which means it was a mage in the Matrix that woke up the second AI. Twist didn't like going into the 'Trix, though (old 1e magic/matrix interaction reasons), which means Morgan's fascination fixated on Dodger ... and, of course, Morgan was the second AI.
Truth is, it would be very, very difficult to actually involve her in every single major thing that happens in the shadowrun world, just because there's so damn MANY things happening all the time. And while you're going along, maybe she's inspired to have her character dedicate herself to something that pulls her away from everything else - a bug hunter, or a toxic fighter, or an explorer of the Deep Metaplanes.
(Note that the second 'interaction' is the big, blatant one - Winternight, Pax, Deus, and Crash 2.0.)