I have a different theory about Geary. He seemed to be in Michael's pocket after he was set up in the brothel. That's probably why he showed up in Havana. But I also think he was plotting his revenge:

We see Geary as a dunce because he thinks with his dick. But Geary is a politician, and politicians definitely know how to be two-faced. And he was at his most two-faced at the Senate hearings. When he says, "These hearings on the Mafia are not a reflection on the great Italian people...," who does he mean by "Mafia" if not Michael? And when he says it'd be a "shame if a few rotten apples were allowed to spoil the whole bunch," who does he mean by "rotten apple" if not the witness in front of the committee--Michael!
Geary also was helping to set Michael up for a fall. Roth, but not Michael, found out that Pentangeli had survived the attempted garroting and was ready to squeal. He reached for Questad, the Senate lawyer "who belongs to Roth." Questad convinced the committee chairman that they could use Pentangeli to trap Michael. The committee chairman arranged for the FBI to take custody of Frankie from the NYPD, and to keep his survival secret.
As a member of that committee, Geary knew Pentangeli had survived and was ready to testify against Michael. So, when Willie Cicci testified before the committee, Geary asked Cicci a question that seemed to be helpful to Michael: Did Cicci ever get a direct order from Michael, or was there always a buffer in between? Cicci says, "No, I never talked to him."
Aha!, thinks Michael. The committee's numero-uno witness, Cicci, has testified that he never got a direct order from him. Now it's safe for him to deny any and all of the committee's charges against him, because there are no witnesses who can testify that they ever got a direct order from him. Thus,Michael lies five times under oath. Unlike Geary and the rest of the committee members, he still doesn't know that Frankie's waiting in the wings to nail his ass.
Bada- bing! The chairman produces Frank Pentangeli, who's ready to testify that he did get orders from Michael to murder, etc. Oh-oh: Michael has opened himself to five counts of perjury. The beauty of it: Michael doesn't have to be tried and convicted of the charges that the committee accused him of (murdering the heads of the Five Families, killing Sollozzo and McCluskey, running all the gambling in America, etc.) They don't have to: they've already got him on five counts of perjury, each of which carries a five-year sentence! Geary's seemingly helpful questioning of Cicci had, in fact, set Michael up for those charges.