I would say: no. I have found that it is possible to "feel" (on a good basis) such a "match". And since behavior patterns and behavioral development through ontogeny IS biological, your conceptualization of cognitive-developmental psychology -- as it actually occurs/unfolds -- should have some characteristics of biological things, AS THEY develop and adapt.
[ For example: Regarding key functioning moving development "forward": one should see definable types of behavior patterns which are supports-for, KEY behavior patterns "behind", AND those that are "forerunners of/for" elaborations, integration, and consolidation AND these should have a definable regularity, characteristic of a biological adaptation process. (I try to show the way with the "A Human Ethogram ...", using all the terminology of classical ethology (the BIOLOGY of behavior) AS INTENDED (as defined). (Click my name to get to my Profile and see this paper under Featured Research, Research Items -- and also see the "Human Ethology and Development (Ethogram Theory)" Project, under Current Research, Projects -- just start by noting this Project's description.)) ]