Well, Let's look at actual Earth history as a guide. The Klingons, when Trek was started, were supposed to represent the Commies, the Reds, you know, the "evil empire". As times changed on Earth, so did the relationship in Trek. Praxis was Chernobyl, Gorkon was Gorbachev. (And I can't believe I never realized it till just now despite the same 3 first letters.)
So the likliest scenario that I see is that some Klingon planets will break away and perhaps join the Federation individually, just as some former Warsaw pact members are now in Nato. You might even get some "erosion" at the core, but I doubt that the empire proper would ever join or merge with the Federation absent some common and ongoing threat that would force a generations-long cooperation between them.