right, all you have to do is get your account approved. Then you can put your code on any of your websites. They don't need registration. HOWEVER. if those other sites don't meet the ToS you stand to lose the account, and with it the sites that DO meet the requirements
you should take care of your website's content... because it's not ok if you have one account... a good website from which you're earning good money, and when you'll add second one get that the whole account disabled. be careful what's your content like.