One friend tried this method once and the bank returned the documents with apologies and instructed my friend to travel and open the account in person.
Extract from "USA PATRIOT Act of Congress that U.S. President George W. Bush signed into law on October 26, 2001"
Banks must identify all the nominal and beneficial owners of any private bank account opened and maintained in the U.S. by non-U.S. citizens. There is also an expectation that they must undertake enhanced scrutiny of the account if it is owned by, or is being maintained on behalf of, any senior political figure where there is reasonable suspicion of corruption. Any deposits made from within the U.S. into foreign banks are now deemed to have been deposited into any interbank account the foreign bank may have in the U.S. Thus any restraining order, seizure warrant or arrest warrant may be made against the funds in the interbank account held at a U.S. financial institution, up to the amount deposited in the account at the foreign bank. Restrictions were placed on the use of internal bank concentration accounts because such accounts do not provide an effective audit trail for transactions, and this may be used to facilitate money laundering. Financial institutions are prohibited from allowing clients to specifically direct them to move funds into, out of, or through a concentration account, and they are also prohibited from informing their clients about the existence of such accounts. Financial institutions are not allowed to provide any information to clients that may identify such internal accounts. Financial institutions are required to document and follow methods of identifying where the funds are for each customer in a concentration account that co-mingles funds belonging to one or more customers.