Well, it should, as you are getting the font from Google ... although Google fonts are a bit wobbly in my experience.
As an aside, make sure to include some other fallback fonts in your list to have some control over what people see on computers where the Google font doesn't work. At a minimum, something like
font-family: rockwell, serif;
font-family: rockwell, "times new roman", georgia, serif;
FontSquirrel has a great selection of web-ready fonts that you upload to your website and serve via @font-face, which has solid support across modern browsers (even IE).
As an aside, you are using some really outdated code there, like <font> etc. You have some homework to do.