A Google AdWords Help thread has something that is obvious to you and me, but when said out loud by a Googler, it makes you smile.
In short, an AdWords advertiser was suspended from the ad network. He then innocently asks if he can still use the domain for his organic SEO purposes to rank on Google. A Googler responded that he can.
Google's Kathleen said:
Yes, you can run an AdWords Suspended URL through SEO. There is no correlation between the two.
Indeed and the quality and spam algorithms are also completely separate.
You have suspended AdWords domains doing just fine in SEO and you have penalized organic domain names suspended on AdWords.
Forum discussion at Google AdWords Help.