Not easily. You would need to overwrite the page_link token method and also alter the handler for the URL requests. I've not attempted this approach, so I can't help with any specifics.
In our case, we use $URL_ALIAS in place of $PAGE_LINK, which means you can use anything you want (as long as it's unique). However, this also involves some work to remap the relevant .page path to it's appropriate alias via the site map.