Can NOI.DAT data be Accessed Through an API? 

Yes — the NOI.DAT report (Notice of Invoice) is an FTP-delivered data file.
This same data is available through the GetTransportationInvoicePayments endpoint in the Billing library.

These reports contain data similar to what is shown in ARB110R1 in the Reporting App on the Magellan Portal.

Below are two mapping tables that show how fields in the existing report correspond to the related API field names.