Its a quite usual practice for companies to have internal auditors.  A large company like BGE had about a dozen or so internal auditors, doing various internal checking of adherence to procedures and internal controls.  Included visiting and doing audits of the operational Depts.  Included surprise audits of petty cash funds at various locations.  Grass roots kinds of reviews.  And when the word gets around that this kind of checking up is going to occur, it puts an awareness into the organization, into the culture.  A good addition to OP's culture.    

An Internal auditor may sometimes become aware of some lagging performance areas, and make confidential feedback to management.

This differs from the kinds of things OP's Director of Finance is already doing.  For example, balancing of bank statements and deposits, --Yes those kinds of things are regularly done by central accounting.  Another example is overseeing the other central financial functions like payrolls and accounts payable, also as would likely already be occurring, centrally under our director responsible for finance and accounting.