Can I 'win' with all my crew on board the destroyed final ship?
Solution 1:
You win.
You would also unlock the "Trustworthy Auto-Pilot" achievement for "[defeating] an enemy ship with all of your crew aboard it."
From the FTL Wikia: "However, it is possible to get this achievement by destroying the final boss with all of your crew on board the enemy ship, resulting in a win with no crew."
Source: http://ftl.wikia.com/wiki/Achievements