I presume the role is to soak up the HI that is formed. Why not other bases such as triethylamine? Is this because the quaternary ammonium salt could be formed? Would other non-nucleophilic or inorganic bases work (for instance, k2co3 or DBU)?
http://www.commonorganicchemistry.com/Rxn_Pages/Alcohol_to_Halide/Iodide/Appel.htm