I have a site that was banned on adsense two years ago that's still doing well on Google search.
It's just lying fallow while bringing in traffic that am unable to monetize.
So, to your question; there's no link between Google adsense and ranking on the Google search.
Afterall adsense still approves sites that are no where close to ranking on the SERP.
glad to hear, man. Even when I was making money with Adsense in 2010-2011 they still seemed too restrictive to me. I don't know why, I might not even be right, but it's the feeling I got from using Adsense. And then... I got fed up with the few bucks they were sending me and I started buying clicks. I don't remember exactly but if I do, I remember that I even received a few checks before they caught me, but the biggest check at that time (701 Euros) had been denied (and my account closed) FEW HOURS before the money being released. I have been devastated, literally. I stood there in front of the "Your Adsense account has been banned" message, unable to login to check if they have released the payment for like 3-4 minutes straight, with a sour taste in my mouth. After that moment my will to continue making money online and to live in general (yeah, I've been pretty weak, mentally, at that time) had died out. Took me few years to recover.
But anyway, I digress... the good thing is that even if they will close my Adsense account again I can still make money off those sites. That's really really great news

... And no, I don't intend to buy clicks again cause I need long-term income this time and I'm not willing to risk anything anymore, but it's google, and - just like amazon - you never know when they decide they don't want us anymore
Also, why are you unable to monetize your site? Amazon / ebooks are always good alternatives... well, amazon not so much, but still. At least you're making something. Also, yesterday I have submitted the 2 websites that I have to hooliganmedia and those guys brag a lot about how their earnings are better than adsense and how they are a better adsense alternative in general. Might want to give them a try (but beware that they're manually checking your website and since their queue is pretty long you will have to wait few weeks to get approved)