Total Amish population is 350k even at 100% growth rate for 5 generations, that population would sit at less then 12 million. It would take another 12 generations or 300 years for that population to surpass 1 billion people, assuming consistent growth of 100%

The issue is that an agrarian lifestyle does not scale to those numbers. So the likelihood of that outcome is low to non existent. 

Also, the Amish are not independent of electricity. They actually do produce and use electricity, so your entire comment is invalid anyways.