Can a parody be published?

If it's based on someone else's work, Ты can't make money off of it unless it's public domain (like Alice in Wonderland) или Ты have permission from the creator of whatever Источник 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 Ты probably could not Опубликовать it professionally или make money off of it, but Ты could still post it to a fanfiction site like AO3, FFN или Wattpad.