Q: Is Parshat Mikeitz ever not read during Chanukah?
A: Yes, in 353- or 383-day years beginning on Shabbat. The Shabbat start means that Bereishit isn't read until a full week after Shemini Atzeret (so the whole Torah reading cycle gets off to a relatively late start), and the deficient year (Cheshvan has 29 days) means that Chanukah comes sooner than otherwise. In those years, the Shabbat during Chanukah (on day 2) is Vayeishev, and Mikeitz is the day after Chanukah ends. (In 355- or 385-day years beginning on Shabbat, Cheshvan has 30 days, so Chanukah starts one day later, and contains two Shabbatot: Vayeishev and Mikeitz.)
Overall, this occurs in about 10% of years, but during the current decade, there's a drought. The last time the actual haftarah for Mikeitz (the famous story of Solomon offering to cut the baby in half) was read was December 2000, and the next time will be December 2020.