If I said Shnayim Mikrah a week early, (I.e. on Shavuos I said Parshas Naso), was I Yotze?
According to Halacha, yes. You may begin from Sunday a portion of the Parasha that was read Shabbos Mincha.
Nonetheless, according to Kabbalah it should be read only on Friday, the day before the entire Parasha is read from the Torah.
שו״ע אדה״ז רפה, ה-ו.