I can confirm that for my case - when I (female) removed my picture from Okcupid, it had the (desirable, then) effect that I didn't get any messages whatsoever anymore, over the space of ~6 months. I might have gotten a non-zero amount if I hadn't stated on my profile that I wasn't looking for relationships at the time, but even with that clear statement I still got messages every once in a while during the time I had the picture up. I didn't try experimenting with a more/less attractive picture.

I got the impression that many people just look at the profile and don't even check the relationship status at the top of the profile.