Yes, "auto" is the default (initial value) for height (at least in most common browsers). Look up the relevant parts in the Mozilla Developer Network or the W3C's CSS 2.1 specification.
In your concrete case you might override one definition with the other. To make sure the one in the file counts, you could add "!important" to the css code in the html file:
body, html{
height: auto !important;
}
PS: I highly recommend getting familiar with proper web development tools like Opera Dragonfly, Chromium's Developer Tools or Firebug in Mozilla - particularly Chromium's Developer Tools show you which CSS rule counts and which rule is overridden by other rules.