Very interesting, TAA. I wonder if you have read Gödel, Escher, Bach, by Douglas Hofstadter. In particular, I am thinking about a section where he discusses the emergence of a mind in an ant colony where the ants work as social units similar to neurons. If you haven't read GEB, I highly suggest it. Hofstadter has laid a lot of groundwork in this area of intelligence as an phenomenon that emerges from parts lesser than (and arguably independent from) the whole.
But, that leads to a question I have. IMO intelligence is in the eye of the beholder, and from a certain perspective, we could say that a Global Brain already exists. I wonder what measures you might use for calculating the evolution (or emergence) of a GB, and in what framework does the Global Intelligence operate? Also, to what extent will the GB depend upon our higher intelligence, and to what extent will it exist independently of us?
Also, you mention that we might be able to predict the evolution of the GB. Does this include a singularity scenario?
Finally, I'm not sure I agree that only crystals exhibit non-living, non-random behavior. I think by that measure you could say that all objects exhibit non-random behavior in their gravitational interactions. You could probably extend that to the atomic forces, quantum systems, rivers, etc. There are lots of non-living processes where entropy is reduced within the observed system, but increased overall.