I know that your companions can work on crew missions while you aren't playing, but does that also include one of your character's companions working on crew missions while you are playing a different character?

 

The reason I ask is that it seems like it would be a good idea to give my main character two gathering skills since I'll probably be playing him the most and then give two mission skills to an alt character and have the alt's companions do crew missions while he's logged off.

Crew assignments have time to complete requirements. Once you send them out to work, they won't return until the time has elapsed. This time does run while you're off doing other things or not even logged in. You can give your orders, log off for the night, and return the next day with the tasks complete. This is the same if you're logged into a different character: The clock is still running, and they're still working. Hope that answers your question. Edited December 15, 2011 by mmsock

Also you can que them up to 5 tasks. Assuming you have the mats/credits for it.