Ignoring the technical question, the social issue sounds impossible. Your problem is when two or more people share one session id right? Well if the session id is in the url, you're going to have this happen a lot, not just from search engine links.

For one thing you're never going to have an exact list of all the search engines. Another problem is people copying the url to each other, via IM, message boards or those public bookmark lists. Those are all going to include the session id in the url. Theres really no good way to store the session id in the url. If you want it to be restricted to one per person you should use cookies.