Not really. Complexity theory deals with many different forms of computation, from Turing Machines to RAM models to circuits to quantum computers. These are all particular concrete artifacts that we use to study the fundamental notion of computation itself.
Saying that complexity theory studies "man-made things" is like saying that chemistry studies man-made molecules. It's technically true, but it confuses the methodology with the object of study: studying particular chemicals vs the underlying laws governing them or particular models vs the underlying laws of computation.
Saying that complexity theory studies "man-made things" is like saying that chemistry studies man-made molecules. It's technically true, but it confuses the methodology with the object of study: studying particular chemicals vs the underlying laws governing them or particular models vs the underlying laws of computation.