No, the pearls are not Mikimoto. The clasp is definitely not a Mikimoto clasp. The clasp seems to say "N...." I can't make out all the letters. That could just be the brand of the clasp, though, and not the maker of the pearl necklace.
However, the pearls are also very dirty and need to be restrung. I bet if they were washed and restrung, they'd brighten up and be a beautiful strand. The clasp could also be polished after being cut away from the rest of the strand and before restringing it. Or you could replace the clasp with something nicer.