Given the strength and (presumed) size of the Klingon Empire, would it really be the Empire joining the Federation? Or would you see instead more of a merging of the two into a whole? Why would the Empire with hundreds of star systems become a member of the Federation council where they are on equal footing with species/races than have only a single planet?
Well, most of those star systems are probably conquered worlds. If the Federation was ever to let them in, the Klingons would have to relinquish all those worlds and then it would be just Qo'noS and the Klingon-populated colonies joining the Federation.