If your navigation is not too complex and you don't have a complicated CMS backend, then it would be fairly straightforward to use a simple tabber script to control your navigation, and display each "page" as a separate tab. This way users don't actually need to change pages. If you have the tabber load up each tab from a separate HTML file, then the search engines will follow that just like a regular link. If you load each tab from content stored on the page, then the search engines can simply index that one page for all of the content, but they might not like that they can't link directly to the content since they probably won't be able to link directly to the tab in question (even if it is possible, the search engine probably won't figure out how).
The only thing it will screw up for the majority of your actual site visitorsis the ability to grab the URL for a specific page from the address bar ... and the constant, annoying music.
Although like Alex mentioned, your original question is kinda paradoxical since this isn't possible to do in an "accessible" way.
I had to create something similar for a WordPress theme a while ago. It was a total nightmare to setup as I couldn't use a basic tabber script to do it and actually had to load each new page the old fashioned way via iframes.