It really depends on the bank. I work for one of the largest banking corporations in the world, and CSRs/tellers are not Officers of the Bank. They have limited signing authority (we're talking cashier's checks), but they do not have the ability to sign any document or sign on behalf of the bank (for example, Medallion Signature Guarantee). Only Officers have that ability to do so, as they are specifically trained to handle such tasks.
At my bank, only management (either branch or higher) are Officers of the Bank.