Answer:
If the communication you call an "e-statement" replaces the paper statement(s) you currently use to transmit account information and the disclosures required by Regs. E and Z, then the "e-statement" must meet the same standards that applied to the discontinued paper statement(s). Conversely, if the "e-statement" is added and the paper statement continues without interruption, then the paper statement satisfies the regulatory requirements and the "e-statement" is courtesy information. Your only concern would be that the courtesy copies must not contradict the "official" statements.