I don't think so, no. Last time I went to order a kindle book from amazon.com (which used to be my "local" kindle store, even though I'm in Canada, as amazon.ca didn't originally sell kindles or kindle books) there was a notification that I had to switch to buying them from amazon.ca from now on because I'm in Canada. So I switched sites and found that the books were more expensive and there was less selection as is always the case in Canada so it looks like, if anything, they're getting tighter on tying your geographical location in to where you make your kindle purchases.
If you go to your Kindle account page, then Kindle support, then Managing your Kindle Account and check under tab 'Country Settings', the entry there is what determines if you can purchase via .co.uk or.com
Most kindle books are available on both sites anyhow.
I use kindlenationdaily.com/ to check out good free offers etc, and their links take you to amazon.com ....so all I do is copy the book title into the .co.uk site and more often than not, it is on the same offer eg free
butterfly - if you have actually purchased something from the US site simply by ticking your country as USA then I stand corrected but it is the billing address of your credit card that determines whether you can shop at the US site.
International companies like Amazon has different pricing structures depending on the region. If all it takes is for me to self certify that I am 'American' then this strategy would be unenforceable.