The user account you run your browser under makes no difference. This is about tracking you around the web. If you log into Google as your real identity, it sets a cookie (evercookie or otherwise), then every site you visit with adsense enabled marks your real identity down as having visited that site. You could be running your browser as whatever user you like in a chrooted Quebes VM all in a BSD jail and none of that will do a damn thing to stop this.
It's fairly easy to block the cookie being set in the first place. For example, a combination of NoScript and CSLite does that perfectly. This is a risk for places where you *need* to allow JS and accept cookies. Think Gmail, it won't let you log in unless you accept cookies and JS from gmail.com & google.com. Given their business model is built on tracking you and collecting you personal data, this is a quick optimisation for them.
If you're interested, I updated the entry to make the *two* problems clearer (there's a much bigger than evercookie privacy problem on the iPhone) and what I think Apple needs to do to fix it. http://singe.za.net/blog/archives/1016-Killing-the-Evercookie-Part2-MobileSafari.html