Dan Ghica has a blog post on discovering category theory for primary school children by way of knot theory. Quite charming, I think, albeit not really an answer to your question. Still, I thought it might be worth noting here.
(I came across it when reading Paweł Sobociński’s Graphical Linear Algebra blog.)
Great question! Yes, this was Piaget's project after initially working with more classic structuralism (e.g. his text titled Structuralism). He explicitly mentions Mac Lane's work in his book on understanding functions, Epistemology and Psychology of Functions
I discuss this a bit in my dissertation, but am not familiar with other work that compares ...