Not a page of its own; this wiki is for official works of Garfield. The only way parodies could work would be if we decide to have a page covering Garfield in pop culture, and even that would be limited by officially published works that don't involve Jim Davis/Paws Inc.
Admin here, it's an interesting idea for sure, though if we are to do it, I would not like them as seperate pages, but rather sub-pages of the main Garfield article. Though we'd also have to do the same for other major characters like Jon, Odie, Liz, etc.
I'm not against the idea, though if implemented, things need to be done in a specific way.