Crit is not technically an on-hit effect, indeed. In fact, even in cases such as Nasus' Q (or other auto-attack modifiers), usually you don't crit the ability - you instead crit on the auto-attack segment of the damage, and then have the ability's damage added onto that. The exception is Gangplank's Q, which, as stated, can have the ENTIRE ability crit including the base damage (although Sheen procs will still not be added on at the end, after the crit).
Please don't go. The drones need you. They look up to you.