How much energy do LEGO Technic gears lose to friction?
Nice find. First of all, it is interesting to see the various techniques they use. 

The short answer to your question would be: It doesn't matter. Each gear, axle and all other components bend, stretch and absorb energy. This means that even for normal large LEGO Technic sets, such as the 42055, you have to build carefully and avoid too much pressure to reduce friction.

When it comes to Googol, it will take years to move most of the gears above their tolerance of, say, 0.1 mm. This is why they put the motor to the beginning of each section to show that it works in principle.

So, starting the whole thing will increase tension and some eruptive movements of the gears in the middle will follow. But the gears further down the line will never move.