Could a CNN hear the difference between sound of a pet moving, and a person? "Deep Learning" neural networks are now successful at image-recognition tasks that I would not have expected say 10 years ago.  I wonder if the current state of the art in machine learning could generally tell the difference between the sound of a dog or cat moving around a house, and a person walking in the same area, taking as input only the sound captured by a microphone. I think I could generally tell the difference, but it is hard to explain exactly how.  But this is also true of some tasks that deep learning is now succeeding at.  So, I suspect it is possible but it's not clear how you would go about it.

I have found algorithms to detect human speech (wikipedia:"Voice activity detection") but separating animal and human footsteps seems more subtle.
It is an interesting application. It is possible. You can interpret sound as histogram (2D image) and apply same image processing techniques (CNN) to extract information. Alternatively, you can keep them as phase / intensity values and train a network on top of them (RNN). That is a great idea. Go for it!