No. Consumer protection regulations rarely apply to commercial transactions. You still need some type of agreement in order to send documents electronically...but the "informed demonstrable consent" opt-in standard is unique to ESIGN and your e-communications with consumers. Communications with businesses have to be documented in a manner that's admissible in court (if the relationship goes sour), but the switch from paper to electrons can be agreed under your state's UETA or ESIGN (minus "informed demonstrable consent"). All it takes is a simple service agreement, but it's an excellent idea to review the entire subject of tree-free communication and documentation with the bank's attorney. S/he is best able to advise you what the courts like or don't like...and the last thing you want is to have a judge throw out all your contracts on a technicality.
Any service charge differential for electronic vs. paper delivery of communications is totally negotiable with commercial customers.