Note that Maseches Horayos has 14 dapim. It will be part of the daf yomi cycle this coming Elul 10 - 22 so it is regarded as valid for a siyum. One is thus able to use it for the siyum this year if one can complete it, treating it as a daf yomi. It is part of Art Scroll Talmud volume 54.
Rabbi Hershel Schechter sent out an answer (with translation)
The straightforward answer is NO. The definition of [fast] is the willful refrainment from eating for a period of time while the gums contain fructose and carbs. So as soon as you will chewing gum your fast will break.
The reason behind your fasting is the gladness of god, so you can’t chewing gum while fasting at all.