If the sign-up process includes delivery of initial Reg. E and other required regulatory disclosures, then you must use paper (if it can be delivered timely) or ESIGN-enabled e-delivery. You do not have to use the same method for all e-deliveries. If the method used for statements doesn't work well for account opening disclosures, develop another method. HOWEVER, you must go through the ESIGN demonstrable consent steps separately for each delivery system you use.
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...gone fishing.