I think the function of the scene is to show that in fact Michael was correct when he said to Kay in GF I that senators and presidents are corrupt too.

I think Geary wanted the meeting to put the heat on Michael. He thought he could bluff Michael by talking tough to him, threw in the Sicilian pronunciation of "Corleone" to show he knew damn well what the family was about, and then figured he could pressure Michael for the payoffs.

Michael and Tom of course just made a notation in their little black book. Geary was far more useful to them as a living pawn than a dead body, so they set up the dead-girl-at-the-brothel episode to give them a blackmail hammer on Geary he could never escape.

After that, in Cuba and at the Senate hearings, Geary is an obedient lapdog to the Corleone interests.