Is it possible to play without using Proficiencies at all?
Yes. You don’t need proficiencies to do any of the adventure-related tasks in the game (they are all “built in” by way of the fact we assumed everyone had Adventuring proficiency). Most of the class powers are explained for each class without reference to the proficiency system, and for those that do reference proficiencies you can just use those selected ones.
ACKS without proficiencies plays closely to the old B/X D&D rules.