Sure, Google uses the various accounts to establish common ownership. Once that's done, removing Analytics or anything else will not make Google forget what it already knows.
I removed Analytics from my sites just over one year ago and replaced it with Piwik. I didn't see the slightest difference in my serps as a result... HOWEVER, I left all my sites details in my Analytics accounts, AND made sure I continued declaring all of my sites in my Webmaster Tools account... for the plain reason I want to show complete transparency in which sites I own and control i.e. I'm showing my hand, showing that I have nothing to hide, nor am I trying to...
Now that I've seen my money ranks tank (in favour of copied, out of date cr@p from sites that clearly game the system), I realise just how woefully naive I've been, to believe this would protect me.
Those $3 articles written by software are doing better than content written by expert in the area
I'm also seeing this... copied, rewritten articles, or grossly out of date/old articles from the depths of history. There is something deeply, deeply wrong with giving preference to very old content, just because it doesn't have ads.
Sorry folks - I had to remove a block of discussion from this thread because it was a direct review of a member's website.
Now I got paranoid... I hope it wasn't my site :-D