No as long as your printer is still physically connected to your computer, it is considered 'local'. The page in the web browser is just the administration tool of CUPS which allows it to be configured regardless of what Desktop Environment you have installed (Gnome, KDE, XFCE, Awesome etc). Many Desktop Environments provide their own tools which interface with the CUPS system directly themselves however some have been unreliable or buggy for any number of reasons. (Gnome in particular comes to mind, but that's primarily because it's what I use myself). That's why the page running on localhost (which is your machine) is used and the preferred method in Sabayon Linux.
In CUPS when you're prompted for a username/password when you choose to add a printer, it is to either add the printer as root which makes it available to your entire system or your standard username which would only allow your user to access the printer. Generally you will want to use 'root' and whatever root password you set when installing Sabayon Linux on your system.
If you set an allowed user and set it to your hostname it would mean that only a username on your system with the same name as your hostname would be able to use the printer, which would be why you receive the message that you have no default printer for your user.
For example, if your computer name (hostname) is "My-Comp" then only a user on your computer with the username (login name) of "My-Comp" can print. If you have this setup, you will need to modify that on the printer settings.
From the CUPS main page (http://localhost:631
) Click on "Printers" along the very top right navigation bar. Then click on your printer. Under the administration dropdown menu, click on "Set Allowed Users". Delete anything in the 'allowed users' field and hit "Set allowed users".
Once you've done that you can also make sure your printer is the default (it should be anyways but doesn't hurt) by selecting "Set as server default" from the Administration drop down as well.