Sure, that's quite possible. It all depends on what the programmer has decided to call the session. It may also be passed along in a cookie or hidden <form> value, but you did ask about the url here I guess so we'll stick to that for now...
The default session id in PHP is PHPSESSID [php.net], so the url might look something like
Well, I have a script that needs to access some info on a site that has cookies. There are pages on the site that you cannot access if you do not have the cookies....so naturally the script has to somehow extract session ifno and append it to the url...or so I presume.
Is the destination page outside of your site in which case the bog standard PHP cookie handling doesn't help? You might need to encode the arguments on the URL such as example.html?arg1=value1&arg2=value2