Does potential difference exist between Earth ground in geographically diverse locations?
Short answer is Yes.

The differences in geology (chemical, water content, magnetic (Earth's magnetic field), electrical disturbances (including lightning), physical stresses) mean they are different. 

Remember the Earth is a rubbish conductor (mixture of insulators, semiconductors, conductors and liquids in random proportions from place to place) so if you tried to harness this I believe you won't get much consistent power.

You might get a huge magnetic input of power during a solar storm due to the changing magnetic field of the Earth as it interacts, but until we can store such unpredictable power, it is of limited use.