In the Keter Yerushalayim Tanach (published by Hebrew University), parashat V'zot Habracha is divided into seven aliyot (aliyah 7 being all of chapter 34 of Devarim.) I don't see this in the Stone chumash or the Simanim tikkun. Simchat Torah never falls on Shabbat, so we don't ever read 7 aliyot for this parashah outside Israel. Even in Israel, my understanding (perhaps wrong) is that when Shemini Atzeret falls on Shabbat, the 7th aliyah is Chatan Bereishit. So why does Keter Yerushalayim show 7 aliyot for V'zot Habracha?
My Simanim Tikkun does have seven aliyot marked in V'zot Habracha (the sixth starting at "Meona", and the seventh at "Vaya'al Moshe"), but perhaps this is because it is the Israeli version of the tikkun. All other tikkunim I've seen (in Israel) have seven aliyot as well.
The custom I've seen, when Simchat Torah falls on shabbat, is to indeed add an extra aliyah before Chatan Torah (making Kol Hana'arim start from "Meona"). It really isn't necessary, as just the normal aliyot are seven+maftir anyway, and in any case, far more than seven aliyot are read; I think it is more of a way of marking the chag that falls on shabbat as special, to add another "shabbat" aliya, as we do on other holidays. I think I've also seen times when this wasn't done - mostly because the community wasn't sure what to do, and the custom isn't 100% clear. The Mishna Berura doesn't discuss this point, though it discusses Simchat Torah reading both inside and outside of Israel, and outside of Israel on shabbat.
Simchat Torah does fall on Shabbat in Eretz Yisrael from time to time. ArtScroll does indeed point out 7 aliyot, saying the 6th is added on Shabbat and starts at "Meonah" and the 7th, added on Shabbat, starts at "Vaya'al Moshe".
Sephardim make 5 aliyot + Chatan Meonah (which ends just before Vaya'al Moshe) + Chatan Torah (which starts over from the beginning of the parsha) + Chatan Bereshit + Maftir, regardless of what day of the week Simchat Torah falls on.
Besides the reasons given in the other answers, the division into aliyos is for purposes of dividing up the study of the chumash (e.g. sh'nayim mika v'echad targum or Chok L'yisrael) into days of the week. I'm not sure how this plays out for "V'zos Hab'racha" specifically (since the "week" is more than seven days), though.