Yes you can... Did exactly that this morning and I'm still doing all the quest components. Gained 1000 rep under FWC then changed right back to dead orbit, and quest like was still there... Granted I didn't have to switch from dead orbit to FWC this morning to rank up, as I switched last week when Paradox was the daily. Though with the one switch a week rule, I could see you not being able to switch back if you had to join FWC this morning.