I'm fairly certain that it should. Do you have the phone in your case? is the 5W charging the phone? With the smart battery case on, if you are using the 5W, it will charge the phone first and once the phone is fully charged then it will start charging up the SBC.
You need something greater than 5W in order to charge both at the same time. More likely you need a charging brick that is a PD, then it will charge the phone and the case at the same time.