deadsea - 10:06 am on Apr 8, 2013 (gmt 0)
I also just did some testing with live HTTP headers. I searched for something that was likely to have HTTPS only sites in the search results, and I clicked on one with live HTTP headers recording everything.
When logged in, even when I click on a HTTPS site, the referrer that Google sends does not contain the keywords. Like Lucy, I see a blank q= parameter sent to the HTTPS site.