Guess that answer depends on what online poker site you're playing on. What you consider "rich" to be. Most important is how good of a poker player you are. How well you know the game. How good you are at reading players. Also how much you are willing to deposit/invest into the site/game etc..
Although NoPayPoker is a free site, where you don't need to deposit money on. This site will not make anyone "rich" so to speak. This is the only site that has a chat lobby, so it is more of a "social" site to play on. People come to NoPayPoker to relax, chat with friends, make new ones, and enjoy a game of poker.
As for cashing out from NoPayPOKER...
Yes you can cash out here if you have the allotted number of freeds. If your government allows you to cashout/play poker sites. Have a verified Netteler account, etc..