It'd have to be more like a VM running the OS with the highest market share (Windows), the browser with the highest market share (Internet Explorer), with the most common language used, with the most common time zone of users of the site you're accessing (varies by site and time of day), etc.
Anything else and you could stand out in the crowd. Using Linux or OS X, for example, really make fingerprinting easier for sites, which is quite disturbing.
Randomizing the values of certain attributes, as you've described, may help a lot if more people adopt it and make fingerprinting a futile exercise to those using it. :) If the people doing the fingerprinting see millions being successfully tracked with just a handful they're unable to track, they wouldn't even care. It's kinda like ad blocking. A few do it and it's not seen as a problem. If the majority does it, then the sites take notice. For a larger scale effect, browser makers should get into this. Mozilla, Apple, Microsoft and Google, in that order (with Opera somewhere in the middle), may be interested in thwarting browser fingerprinting.