Short answer is: It depends. Why would you want to release as a private beta?

You probably want users to be able to freely refer your product to friends. You probably want people to be able to discover, sign up, and try your product in one sitting. You probably don't want potential users to lose enthusiasm while they wait for a beta invite. You probably won't have crushing server traffic. If you do, you probably won't regret letting so many people use your product at once.