I was playing Jamian's "The Promised Land," and having just left the entrance to level 4, I hookshotted a hookshot target after using the whistle to summon a whirlwind. While being drawn toward the hookshot target with the hookshot, I made contact with the whirlwind, which was coming from the same direction I was hookshotting toward.
When the whirlwind hit me, Link became invisible. Not invincible, but simply invisible. He didn't leave the screen, I believe. He remains invisible, and is walking around the overworld in a confused state.
Using the whistle and entering a whirlwind again reverses the effect, returning you to your usual happy opaque state.