It looks like that's something they hoped to have in place for 2017, but still is not possible. From the official website FAQ at https://e-resident.gov.ee/faq/

It looks like that's something they hoped to have in place for 2017, but still is not possible. From the official website FAQ at https://e-resident.gov.ee/faq/ https://e-resident.gov.ee/faq/ "Visit the bank office in person and apply for a bank account. The bank will want to know how you are connected to Estonia and how you plan to use the account. You will need to bring your e-residency card along."