You could make it very onerous to move around the site even if you're logged in. For example, after every few links you follow you have to pass another Turing test. That would be completely unreasonable though.

I think once a user is logged into your site, you'd have an extremely hard time defeating this sort of behavior without degrading the quality of user interaction or treading on legitimate use of your site. You may be able to defeat egregious abuses, such as scraping entire photo galleries in seconds, but even that can be defeated by a script that randomizes requests/times between requests.