Yes. Frankie's credibility was shot to hell at that time, but the government wouldn't have given up on Michael. As long as Frankie was alive, there might have been some way the government could have used him against Michael.
So, I'm guessing, the proposition from Michael to Frankie (via Tom) went something like this: "You haven't got any life ahead of you--you're gonna be a prisoner for the rest of your life. Your family will wither without you. Do the honorable thing and your family will be taken care of. If not, you'll be the instrument of their demise." The last word would have had enough threat for Frankie to see reason.