Is there a way, to take out the HTML link and provide a favicon or alternatively, not let it be requested - perhaps using .htaccess?
<link rel=icon href=icon>
For instance, when a user opens a [.pdf] or otherwise, there is no icon - displaying 'nothing' or at least it is transparent. The purpose, is to minimise the number of HTTP requests. You see, I do not want to have [the HTML link] at all - so a data URI is not necessarily an option. In other words, I wish to remove this HTML tag - displaying nothing like a [.pdf] file, in the browser.
If you don't have a tag specifying the url of a favicon, most browsers will just send a blind request to www.yourdomain.com/favicon.ico and hope for the best (thanks to w3d for pointing this out). This isn't something you can prevent them from doing.
Although, from what I know, favicons are cached in the clients browser, so they won't even be sending requests for it on every page-load.