Not if it refers specifically to individual models. Individually, there are Cultists and a Cultist Champion. Collectively, they are a unit of Chaos Cultists. You can't have your cake and eat it too. There are quite a few examples of this in various other codices and FAQs, where one member of a unit can't take certain upgrades because they're a different type of model from the rest of the unit, and yes, GW has verified several of these cases in the FAQ/Erratas.
And your argument that the "can't take options" doesn't apply until you decide it does, and thus you can just write down "35 Chaos Cultist" then go back and erase Cultists and write in Zombies is bull****. By that logic, you may take any and all options available to Chaos Cultists and just completely ignore the "can't take options" rule.