If you look at network activations in higher levels of a convolutional neural network, you will find some units that are activated by the individual parts of the hand. (There is a video out there where they show that for parts of the face, I'll be looking for a link.)

Those activations are a representation of the matched patterns at a similar level of abstraction as the compositional model humans might come up with. They are not exactly the same as what a child would draw, but mostly because the neural network isn't trained to draw with hands. With a bit of work, I'm sure a bunch of PhDs could make a neural network model generate child-like drawings from realistic images.