What is the scope of the drupal session cookie?
Better late than never?

Yes, if you are creating the cookie with a default path. It will use the current page path. So the cookie will be restricted to any path starting with the defined one (if it's /a/b then the cookie will be available for /a/b, a/b/c etc but not /a alone).

(I had a short period of hair-tearing once where I was accessing a site using it's IP address and unable to understand why the cookies weren't available ... they were hardwired to the domain.)