This is probably possible through some extensions and Firefox. The much loved TreeStyleTabs already has an option for "autohide the tab bar". If Pentadactyl/Vimperator don't already have an option for autohiding, it's probably pretty easy to script something up.
Pentadactyl/Vimperator do absolutely have that (set showtabline=never).
I use Pentadactyl, and a Shift-B (show buffers) followed by a <tab_number>gt will get me to wherever I need to go.
This is, of course, not discoverable, and therefore not really suitable for the demographic whose problems this article is hoping to solve, but for someone who's willing to put some time into learning a program (or who already uses vim), it's pretty spot-on. I, for one, love it.
I should add that the problems this article is trying to solve really ought to be solved through a thorough integration of the browser tab-system with the window manager. That, of course, necessitates a thorough rethinking of the window manager, also. But that was the problem tabs alleviated in the first place, right?
No, Chrome's extensions are basically the same as GreaseMonkey scripts (at least, that's the frequent comparison I've heard). Firefox's extensions have the full power of XUL and can radically change the browser.
engage beating a dead horse here
The lack of functionality in Chrome extensions is why I (and judging from the comments I've seen in most Chrome vs Firefox threads, many other HNers on Firefox) refuse to switch to Chrome despite its much touted speed. Until I can get Pentadactyl and TreeStyleTab, its just a downgrade in usefullness.
Some browsers do that in full-screen mode now.
By the way, in Opera you can configure browser that way so toolbars will auto-hide. You can assign shortcut or a gesture to them. Hovering isn't a good idea because it will eaither have to move the page (which is distracting and annoying when you do it on accident) or cover the page (which could block some content). So having it on gesture and/or shortuct would be the best way in my opinion. If you want the toolbarless experience. (I personally don't)
Video player's hidden controls react to mouse movement in the screen area though, a web browser would need a different heuristic — like moving the mouse close to where the controls should be or somesuch.
There's people arguing, of course, that that's really poor usability, because you can't see what you can do. I guess it's a matter of taste as much as anything, and it's probably more of a power-user thing.)
The vast majority of the time, I don't interact with the chrome of the window: the back and forward buttons, the address bar, tabs, etc, so why not get that out of my face while I'm not interested?