Barring some weird bug, you wouldn't be allowed to leave the completed spaceship screen without launching unless the game had already ended by the time you completed the spaceship ("ended" = you already won or lost by any of the other 4 victory conditions or you reached the year 2050 and won/lost based on ending score). If in fact the game had already been won or lost by any method but you elected to play "a few more turns," you unfortunately don't get the opportunity to later launch the spaceship.