Can a parody be published?

If it's based on someone else's work, tu can't make money off of it unless it's public domain (like Alice in Wonderland) o tu have permission from the creator of whatever fuente you're using (typically this means paying for the rights to use the material, if they're even willing to sell).

So in answer to your question, no tu probably could not publicar it professionally o make money off of it, but tu could still post it to a fanfiction site like AO3, FFN o Wattpad.