ES said that if my gmail account was moved overseas on an international server, then the NSA could have a copy of my account even if there were no international sources/targets. Is that true or false?
That's true. While theoretically the NSA is not allowed to monitor communications between two american citizens, in practice, any communication leaving the country is simply assumed to involve a foreigner and is thus up for grabs. This "inadvertent" capture of american communications is in fact standard operating procedure:
The government has set a dismally low bar for concluding that a potential surveillance target is, in fact, a foreigner located abroad. By default, targets are assumed to be foreign. That's right, the procedures allow the NSA to presume that prospective targets are foreigners outside the United States absent specific information to the contrary—and to presume therefore that those individuals are fair game for warrantless surveillance.