The answer to your question is "yes." Here's a quote from the Railpasses section on this site. (Click on the "Railpasses" tab at the top of the page to read more.)
"Passholder fare: Travel with a Passholder ticket must take place during the validity period of a railpass that covers one end of that day's Eurostar route (Britain, France, or Belgium). This trip does not use one of your counted travel days on a flexipass. However, both flexi- and consecutive-type passes must be validated. For instance, if you have a Passholder ticket from London to Paris and a Eurailpass for use on the continent, then you must have the Eurailpass validated at the station in London before boarding the Eurostar train."
However, if you register as a resident of the UK at eurostar.com and book well in advance, you can get a single (one-way) London-Paris ticket for £35, which is cheaper than the passholder fare.