Not only that, but the original idea was to marry Rhaegar and Cersei. There should be a way to control things like: Can only marry into a Great House, or cannot marry into a minor one. Like Littlefinger having to become Lord of Harrenhal to marry to Lysa Tully.
Relations play a role - the other house has to accept your proposal first of all.
I hope the AI will be smart enough to see the strategic benefits of high-level marriages. They do serve as alliances and (more or less?) unbreakable truces, after all. If Lannister and Targaryen aren't on bad relations (Aerys being crazymad and all that), AI-Aerys should look at Cersei Lannister as a favorable match since the Lannisters are most powerful or second most powerful lord-paramount-level rulers of the realm.
The game won't have a character like Littlefinger though, since CK2 is about the plots and actions of high ruling houses and doesn't really have "actors" outside of that.
At the start of the war of five kings, Baelish would be an unlanded courtier with tons of gold but little prestige, sitting in King's Landing, acting as steward for King Joffrey of the Iron Throne. I don't think an unlanded character can start plots, or be invited to them, so the only intrigues he'd be involved would be event-driven stuff that happens within Joffrey's court. Harrenhall could be a holding of King Joffrey, but Baelish would have to be lucky to be awarded exactly that title by AI-Joffrey. Once he gets it, though, he would be a good candidate (among many) for AI-Robert-Arryn to marry his mother
I do wonder how the whole regent thing works. There's been very little information about that mechanism. Lysa Tully would be AI-Robert's regent, but could she be succeeded to that position by a character who's not even residing at the court? (The game would consider Baelish as a resident of Harrenhall, since there's no way to have a ruling character be somewhere other than his capital, unless he's appointed to his lord's office or leading a regiment.)