I don't know the answer to your question ... but I found this on the 1K site. It says you can earn "miles," but I know know if that means EQMs:
You will now have more international destination options in Europe, Africa and the Middle East—and more mileage-earning opportunities—because of United's code-share and Mileage Plus's agreements with Swiss International Air Lines.
Beginning November 9, 2005, United's code will appear on SWISS flights between Los Angeles and Zurich, Chicago and Zurich and connecting flights from Zurich to Dubai and Muscat. Plus, SWISS's code will appear on United flights between Washington, D.C. and Zurich and on flights between Los Angeles and Honolulu. More routes are scheduled to be announced, pending regulatory approval.
The code-share will allow each carrier's passengers to seamlessly connect to the other carrier's flights.
You will also be able to earn miles on all SWISS flights and, in early 2006, you will be able to redeem those miles for award travel. Plus, when SWISS joins the Star Alliance®, you will be able to earn Elite Qualifying Miles and Segments and be entitled to Star Alliance Gold and Silver benefits on their flights.