Does the Legend of Zelda version available from the Wii's Virtual Console service feature the "second Quest" that was accessible once you either completed the game once (or put ZELDA as your name when you started the game)?
According to Wikipedia:
Furthermore, I can find no reference stating that the "Second Quest" has been removed. I would logically conclude that if there is no reference regarding it being taken away, it should be in the game.
We retro-gamers never take modifications to original games lightly.