You could sure do it for multiple domains. Not sure what the maximum is (500 domains or 1,000 ? )
"Place codes in new domains without having to go through review process." - I think it will not work. You have to go through "review process." They will review the new domains and then you can use AdSense on them.
Not sure if I read every word of 1,000 pages of TOS, but I get the general idea.