Why hide the password box, then, unless you think that users learning to type and have magically it go somewhere invisible is a good UI design…
(Interesting aside: I complained to someone on the Mac Safari team that it was difficult to search open tabs, and he told me that apparently this feature already exists! You go into the tab overview, and…just start typing. A little search bar will pop into appearance in the top right corner. Why it couldn't just be there and have keyboard focus from the start, I have no idea…)