Sure, if you want.

Would that require an admin or can we just add it to the page?

Just put your Tear Jerker entry on the Sonic The Hedgehog page.

No, I mean how can we add a tearjerker page to the section dedicated to the archie comic book series instead of the franchise in general?

Just add your examples to this page; you can index it by adding the link to the Comic Book Tearjerker page.