Media Analytics (Heartbeat) data is sent to Heartbeat servers (<namespace>.hb.omtrdc.net) first. These hits are then forwarded to Analytics servers (<namespace>.sc.omtrdc.net) internally. BDIA is meant to send data to Analytics servers only. Therefore, I do not think you can send media analytics data via BDIA.
If you are looking for APIs to send streaming data to Analytics, I would recommend using Media Collection APIs. You can use Track Downloaded Content to upload bulk streaming data in a single call.
Hope that helps.