Personally, I use search all the time while I'm around other people or in a public place, and it would be a bit jarring to suddenly see private emails alongside my results at these times. This isn't a privacy issue per se, but it's just unexpected and I could see it leading to awkward situations for some people (e.g. when someone has someone else run a quick search for him and private or embarrassing emails show up).

If it's strictly opt-in then I don't see a problem.