Yes.

Okay, more helpful answer: He is chaos incarnate in a world with heavy order v chaos themes and in that sense is more of an eldritch being. However, he is canonically referred to as "demon" and "devil" and does the demon thing of being summoned into the human world and contracted as a mercenary. Follows wizards around as their heavy for several hundred years, serves as a general-for-hire to strategists... All that fun stuff.

I'm canonblind to Howl so idk how any of that would read to him.