Rather then a company published manga, can a self-published manga become an adapted anime? Did it ever happen before when self-published mangas become adapted into an anime without having mangas published by companies?
There are a few anime adaptations of doujins and Artist CGs, like Z-Ton's "A Beautiful Greed" and Maron Maron's "Yareruko! Densha Ecchi", both of these are NSFW. Also that short anime "Getsuyoubi no Tawawa" was based on illustrations Himura Kiseki posted on pixiv that later got released as compilations on Comiket, so this is a doujin as well. Those are the only ones that come to mind at the moment but I'm pretty sure there should be a few more. It doesn't happen that often though, it's more of an exception to the norm.