You mean use paypal without it being attached? Sure, it will remain unverified and the only way you can fund it is to get money sent to it from another paypal.
My friend has one named "Juan Valdez" and another real account with his name. He uses his main real account to send $ to his "Juan" account to buy. When he sells, he sends the money from his "Juan" account to his main real account. You lose 2x the fees this way but he's already been burnt by paypal once so he accepts it.