In RoundCube, enter "billy bob" in the search field in the upper-right corner and hit enter. Then look at the web server logs. You will see something like this:
XXX.YYY.ZZZ.WWW - - [01/Mar/2013:12:17:38 -0800] "GET /webmail/?_task=mail&_remote=1&_action=search&_q=billy%20bob&_mbox=INBOX&_headers=to,text&_filter=ALL&_=1362169057912&_unlock=loading1362169057911 HTTP/1.1" 200 260 "http://CENSORSHIP-WAS-HERE/webmail/" "Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.22 (KHTML, like Gecko) Chrome/25.0.1364.97 Safari/537.22"
Now, if you copy that long link, preface it with http://your-webmail-server/ and enter it in your browser, you get an error. Or, at least, I did.
I tried to tweak some of those variables, eliminate some of them. I either get "invalid request" on a white page, or "SERVICE CURRENTLY NOT AVAILABLE" on a nicer page.
Is there an easy way to pass a search URL like this to RoundCube, from an external link? Assuming, of course, you're already logged in to RC.