Derek Sivers explains in a 3 min TED talk, http://www.ted.com/talks/derek_sivers_keep_your_goals_to_you..., that by keeping your goals to yourself, you become more motivated to achieve them (because you haven't made them part of your "social reality"). In the very early stages I suspect that might be the biggest benefit of stealth mode..

staying stealth could benefit in that you are able to build your own product without as much of an outside influence, but for some products, advice from experts helps and could lead you to better opportunities too.