http://www.ct.gov/dmv/cwp/view.asp?Q=557260&A=807 "This new program was approved by the legislature in 2013 for undocumented individuals who are 16 and older and cannot establish their legal presence in the United States. They can apply for a Drive Only license, however, it will not be valid for state or federal identification."
If even the state of CT does not consider it valid for identification, banks might not be so quick to accept it. In order to get this card, the applicant will have had to have shown the state of CT at least two types of ID listed here:
http://www.ct.gov/dmv/lib/dmv/20/29/di-4.pdf A Drive Only card allows for an expired passport to be used as identification. Wouldn't exactly fill me with confidence.