Except they aren't dropping cookies on your machine so it'd be harder for them to track users and that's something that can be verified externally.
However, an adversary can also fingerprint your OS/patch level based on packet structure[1][2] - which can't be easily changed. This will add more identifying bits.
1.http://nmap.org/book/osdetect-fingerprint-format.html
2.http://www.windowsecurity.com/articles-tutorials/intrusion_d...
https://panopticlick.eff.org/browser-uniqueness.pdf
All in all it's pretty scary though. My browser is unique among 5.3 million or something. And then there's the algorithm they mention that can detect fingerprint changes with 99.1% accuracy, and be used to do things like recreate cookies that you deleted.