Nope, this is not possible.
I hope you realize that you are trying to address an extremely difficult problem.
Let's say your url looks like
http://mysite.com/mypage/
If you change the window location programmatically to
http://mysite/mypage/1/
Browser will take over and try to navigate to that page, there goes your fancy ajax code!
So what's the alternative? You use URL fragment.
Let's say you have a URL like this,
http://mysite.com/anotherpage/#section
Browser will first load http://mysite.com/anotherpage/ and try to find an anchor named 'section' and scroll to that location. This behavior is exploited by the 'Addresses' plugin. This is similar to how those 'Scroll To Top' links work.
So if you are on the page
http://mysite.com/mypage/
and change the URL to
http://mysite.com/mypage/#1
Browser will not load new page but rather try to find anchor named '1' and scroll to that anchor.
Even if you have managed to add fragments to the URL, it doesn't mean the work is done. If the user presses the back button, DOM will be reset and you will have to parse those fragments and recreate the DOM. It's definitely non-trivial.