Since a convolutional network applies parameters (filters) to different parts of an image evenly, this means that this approach still learns, except not from a corpus of images, but from the image itself (i.e. one part of the network learns from different parts of the image).

> This makes me wonder whether and to what degree the structure of the brain's connectome might be a necessary prior for AGI.

Convnets have been invented to speed up learning (reusing parameters). The human brain (afaik) doesn't contain such speedup. Instead it relies on massive parallellism of neurons, and thus trains all "filters" separately instead of reusing them. Therefore, I suppose this approach would not apply to humans.