Looks like it's already being done. Somebody had previously posted this:
YouTube - Hod Lipson: Robots that are "self-aware"
The idea of using a physical locomotion device and allowing different neural net configurations to "take control" of the body is interesting: Why model physics when you can use real physics? However, this doesn't account for the possible co-evolution of brain and body.
I'm not convinced by the strategy used in the spider-like robot. While it can be said that we do have some kind of internal model of our body, it is likely a lot less of an explicit representation than suggested by the video. The model probably is nothing above the integration of sensorimotor systems. We don't systematically test our bodily capabilities and then form explicit theories about how our bodies are organized. Such bodily representations have evolved over a very long time, not just through motor systems themselves, but through the interaction of motor and sensory systems.