Or can it not get up on its own yet?
[edit] If you add a thin piece of string to the top and connect it to the top of the room, I bet you can make a mechanism to set it upright when it falls over. Then it has all the time in the world to learn to land on its feet.
There are some research groups trying robotic control with black box neural networks (pixels in, control commands out), afaik with limited success so far, particularly with this many degrees of freedom.
Deep learning has yielded some really incredible results the last 5+ years, but those results have been concentrated in a few areas (computer vision, speech recognition, game decision, ...). So there is a tendency to think NNs can do anything, but really a) setting up a NN to work with a problem is non-trivial (architecture design, data collection, data labeling, feature selection) and b) very much an open research topic for many problems, ie not guaranteed to work at all.