I think Mike would have multiple plans for getting rid of Roth, as Roth did for Michael in all likelihood so if Fredo had blabbed Plan A, Michael would have gone with Plan B. I think he told Fredo about Roth just as a way to try to test Fredo, draw him out.

If Michael had been just a tad more patient at the banana daquiri scene, Fredo might have confessed everything then. I think he was on the verge of doing so.

Michael had, if nothing else, supreme self-confidence. To walk into the Lion's Den with just one bodyguard and an incompetent brother of mixed loyalties showed that. It also led Roth to believe that Michael was still a step behind, which is what Michael wanted him to believe.

I also think that despite everything Michael still didn't want to believe that Fredo was the fink.

"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming

Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.