http://www.japanrailpass.net/eng/en002.html
The people at JR will look for the "temporary visitor" label in your passport before exchanging your voucher for a rail pass. I'm not sure what you get in your passport if you enter under SOFA but I think this means that you have to choose between SOFA and being eligible for a rail pass.
I am not a lawyer, but perhaps with SOFA you could evade rail fares, refuse to pay the fines and then demand to be tried in a court martial rather than under the Japanese legal system. (?) I doubt that it would save you money in the long run.