I think Roth engineered the event to the extent that he conspired with the Rosatos to have Frankie assassinated at their meeting. He and the Rosatos were allies. He supported them in their beef against Frankie over the three allegedly promised territories in the Bronx (per Michael's meeting with Frankie in the boathouse during Anthony's party). Roth probably told them that if they whacked Frankie, they could take over the Corleones' NYC operation, and that he'd "take care of Michael." He probably didn't tell the Rosatos that he was going to have Michael whacked in Havana; perhaps he said Michael would go along with it as a condition of Roth turning his Havana operations over to him. But, Roth didn't--could not have--engineered Frankie's survival. That was strictly happenstance.

You make a good point about too many people knowing about Frankie's survival. Here I have to give FFC some "directorial license":

NYPD was first on the scene and arrested Frankie (Tom: "The NYC detective squad said Frankie was half dead, scared, talking out loud about how you betrayed him"). Frankie was inside the bar, not out in the street where the shootout took place. Perhaps the detectives, seeing that Frankie was ready to rat out Mr. Big, thought it would be in everyone's best interest to keep Frankie's survival secret, the better to protect him against Michael trying to silence him, and to get more info out of him.

The "directorial license" part is how the Senate subcommittee managed to wheedle Frankie away from NYPD. A stretch-guess: The Senate subcommittee already had hearings scheduled on organized crime, and was planning to call Michael as a witness. Roth, through Questad, had the Senate subcommittee chair appeal to NYC's mayor to have NYPD give up Frankie to the subcommittee. The promise would have been that the subcommittee had a far better chance of connecting Michael, through Frankie's testimony, to a greater range of crimes (i.e., running all the gambling in America) than were covered by NYPD's jurisdiction.