GitHub cookies are restricted to github.com and gist.github.com domains (using a redirect trick to allow cross subdomain cookie sharing). You can use all the JavaScript you like on your Pages.
The .github.com cookie is old and useless. You can't use it to do anything - it's a relic of our old authentication system. We should have made sure they were deleted before switching to the new cookie as it's caused some confusion.
What mojombo said is accurate. (He's a GitHub co-founder and I'm the person who wrote the redirect code.)
