I am going to break this down for clarity in my own mind, if not in the minds of others. By definition "enlightened cognition" means that one is "freed from ignorance and misinformation" in order to pursue "the mental action or process of acquiring knowledge and understanding thought experiences and the senses" (quotes from a couple of dictionaries). So to paraphrase, is the acquired knowledge and understanding of wisdom, in any Buddhist tradition, more than its parts? Wisdom, is insightful understanding. Simple put the question seems to be, is wisdom more than its parts?
Alright, now let's add the comment's reference to "direct realization of reality", which from the Buddhist view means Ultimate Reality, the direct realization of emptiness which leads to the end of suffering completely which is enlightenment, or buddhahood.
Both Theravada and Mahayana Buddhism translate Prajna and Bodhi as Wisdom. In the deeper sense, Prajna is insightful understanding; and Bodhi is the perfection of wisdom, or the teaching that all phenomenon are empty of self essence, which ties back into the direct realization of reality.
This also takes care of the "in any Buddhist tradition" part of the question.
Is wisdom more than its parts? In the mundane world it is not, since one accumulates pieces and parts of wisdom, conventional wisdom, without sensing a higher pursuit. However, upon the realization of Ultimate Reality, the parts cease to play a role as they too become impermanent through emptiness.