I haven't seen a lot of information on NERD progressing to Barrett's since NERD is supposed to be an 'abnormal' reaction to normal levels of acid in the system. But any form of acidic substance that 'invades' and changes the pH of the less acidic tissues of the esophagus could result in problems. Many docs feel that using PPIs for NERD works well since it will cut back on the amount of acid produced and therefore less acid will reach the esophagus.
I hope your son will follow-up on the EoE. Encourage him to work with a doc who understands how food sensitivities can impact the body. EoE can be extremely debilitating.