That's correct, you can continue the game as long as you have any capital ships left. They have plenty of room for a shipless captain... As a matter of fact you can assign any capital ship as the "flagship" in the formation screen. Fighters on the other hand just don't have the means to rescue you.
In the full game you can choose one of the three missions (Scientific, Pirate and Military), and each one gives you a different ship to start with. You can also find a particular "alien" ship that probably deserves the flagship status
