Rav Meir Mazuz in Mekor Neeman page.109 was asked this question and he answered that if one finishes one of the books(Maadah,Ahava...) then it's considered a siyum. He brings the Shu"t HaRashbash siman 52 that one who learns halchos from the Rambam every single day is muvtach that he is a ben olam habaah.
In Guidelines by Rabbi Elozor Barclay and Rabbi Yitzchok Jaeger, both for the 3 Weeks and for Pesach, they say that to make a siyum that permits meat & wine in the first case or breaking the fast Erev Pesach, it must be on one of the following:
A seder of Mishnayot (Zeraim, Moed, etc)
A masechet of Gemara
A sefer of Tanach learned b'iyun (which they do not define)
A chelek of Shulchan Aruch
So, at least according to them, no, a chelek of the Mishneh Torah will not suffice.