I'm in the middle of building a list using Ezra in the Sheathipede shuttle with sense. Can I still use sense in the system phase while he is still docked to VCX-100?

Nope. Docked ships are out of play for all purposes, except for the occasional card the specifies an effect based on their existence, specifically the Escape Craft pilots, and the Ghost's ones. Only the things that specifically call out effects whilst docked, work whilst docked.

Except that they do still regain recurring charge tokens.