Since it's just a rebranding of DoubleClick's Performics affiliate network if you've used Performics you've used Google Affiliate Network. Right now I wouldn't think that being banned from AdSense would keep you out as the sign up process is identical as when it operated under the Performics brand, maybe when the two become a little more integrated it will be an issue.
I love DoubleClick/Google Affiliate Network They are prolly changing their systems to detect banned people, but maybe not just yet. So hurry up and apply quick quick!
I heard that was B.S. It's been awhile but I look on Google's site and they said there was no such thing,
Google Affiliate Network publishers can now easily browse across relationships to find products and build links to specific products. The product search feature allows publishers to access aspects of the advertiser’s product feed within the Google Affiliate Network interface. Publishers can view product price, image, category and description in addition to tracking and creative urls.