It should be enough to get you the balance of what's in the account if the affidavit of heirship establishes you as the only heir. It will not get you what happened prior to her death.
In practice, it's up to the bank. The banks usually won't accept them, as it creates liability for the bank. If you really want to find out what happened, then you would have to apply for letters testamentary (if she had a will) or letters of administration (if she did not have a will.) These procedures will allow you to step into your mother's shoes and do anything she could do, such as ordering bank account records, etc.