If you are asking if the Japanese version of King Kong vs. Godzilla was ever presented in mono, then yes. Toho created both a stereo and mono version of this and their other early stereo films. I would guess that these mono versions were also used for the many later re-releases these films got too. There are also sources available for the soundtracks in Mono, which Toho Music has released.
However, if you are asking if the mono version was ever released theatrically in 1962 alongside the stereo version, then that is a question someone else will have to tackle.
If it bites... don't mess with it!