The processing of that non-visual input will still be performed by the visual cortex.

It certainly won't be in sighted individuals, and I doubt it can be adapted as you suggest in blind people. The visual cortex is quite specialized, and performs quite low-level image processing, e.g. detection of edges and corners, as well as movement. It does not do any object recognition. That's done elsewhere. For example, the fusiform gyrus is involved in facial recognition.

A good introduction to how the visual cortex works can be found in Eye, Brain, And Vision: http://hubel.med.harvard.edu/book/bcontex.htm

For example echolocation (in humans, not bats) is done in visual cortex[1]. Visual cortex shows activity during dreams and imagination. Blind people do use their visual cortex.

[1] Sorry, don't have a cite, but there are a lot of results on Google talking about it: https://archive.is/iDE27

This doesn't surprise me. They are using their visual cortex to process sensory data (auditory images) which substitute for sight.