I know that sitting in an asteroid field once you've dealt with the event there can level up the shield skill for a crewmember; they gain XP by restoring shield points, regardless of whether an asteroid or an enemy weapon damaged the shields.
When an asteroid misses me (the ship dodges it), do the crewmembers manning the Pilot & Engines consoles gain XP for their respective roles?
They do gain XP - you can hover over your crewmembers on the left hand side and watch as they gain XP. The reason is as follows: the primary use of pilot and engine is to increase dodge chance. As you've probably noticed already, leveled up pilots and thrusters means higher dodge chance. When your respective crewmembers achieve their purpose, such as repairing shields or firing weapons, and in this case, dodging stuff, they gain XP. Hope this helped!
