Is the increase of drag compared to zero-lift drag called "induced drag" in case of an infinite airfoil?
I think you'd need to be a lexicographer to get excited about this one.
If you take "induced drag" as being literally "the drag associated with the production of lift", then you would have to say yes.
If you prefer McCormick's version: "Induced Drag: The drag that results from the generation of a trailing vortex system downstream of a lifting surface of finite aspect ratio" then pretty much by definition, you'd have to say "no".
I prefer the latter.