It's like making your phone number 'unlisted'. People looking through phone directories may not find you, but there are so many other ways to get the same information.
Privacy protection on a domain name is like locking the front door of your house. It will keep innocent people out, but will be useless protection from anyone who really wants to gain entry.
Likewise, there are MANY ways to learn the details of domain ownership. I'll list just a few basic ways here, but realize there are many other tools available to get the information you need.
Here are a few simpler ways to determine domain ownership:
-- Every whois record has a proxy email address in it. Even though it is not the domain owner's actual email address, anyone can use this proxy email address to send the owner a message. You can use this to ask a question the owner would be eager to answer, like, "Where can I buy your [product]?". When they answer, chances are the email you receive will reveal their real contact email address. You can then search Google for this email address (in quotes) to see other websites they may own.
-- You can contact their webhost, and complain about something on the website (if appropriate). It's easy to learn who owns it this way.
-- If they sell something from the website, you can purchase from them and you'll have their PayPal email address or other merchant info.
-- You can look up an older version of the website by using Archive.org or
Whois History: Historical Whois Lookup | DomainTools, and see the previous whois information (before the privacy was applied).
-- Do a reverse WHOIS search (Reverse Whois Lookup | Domain Ownership Search | DomainTools).
-- Do a reverse IP Lookup to see other domains that are hosted on that server. This can reveal other websites owned by the same person, which may not be privacy protected (Reverse IP Lookup | All Names Hosted at an IP | DomainTools).
-- Based on their domain name or any other info you may have discovered, see if they have a presence on Twitter or Facebook. "Like" them or try to "Friend" them. Message them with a question or two. Each little bit of info you discover can help with the bigger picture.
-- In serious cases, you may be able to leverage the Freedom Of Information Act to force information.
There are many other ways, but the point is, a little creativity can get you the information you need. Any little bit of information you discover, whether it be name, email address, other websites, nameservers, phone numbers, addresses, can be searched in Google using "quotes" to lead you to further information.
Should you use Privacy Protection? Yes, if you just want to avoid contact with casual passers-by. No, if you think it will prevent someone from getting your information if they really want it. No, if you're trying to instill confidence in your website visitors.