No, I'm referring to "external-accessory". This works with both dock connector and Bluetooth iAP accessories. You're right that the other one is only for BT LE (4.0). It's understandable that many people are confused about the CoreBluetooth vs MFi Bluetooth.
if inPulse has the Apple MFI authentication part on-board, then yes, they can talk Bluetooth 2.1 to iOS devices, from a backgrounded app.