Yes, some browsers start downloading /favicon.ico, at the same time they start downloading an HTML document. If there is no file, you will receive an additional 404 in your server log, and the browser will have to make an additional HTTP request when it finds out that the icon is in a different place.
Quote from Yahoo Best practices for speeding up your website :
favicon.ico - , . , , , 404 Not Found. , cookie , . , , IE , .