I'm not sure why the Klingon Empire would join the UFP. They have their own system, rules and codes of conduct, many of which just don't fit in with Federation principles. They have a massive expanse of space with is older that the Federation, and their alliance to the UFP has proven to be both mutually beneficial (SEE: Dominion War 2373-2375) as well as being a hindrance to their warrior mentality (SEE: Federation-Klingon War 2372-2373).
I think there would be a few more Klingons sign up for Starfleet, a continuation of the alliance with many partnership operations, but I would think the two would remain separate entities.
But that's just me.