No, the reason is that your audio source needs to be connected to the inputs of your subwoofer's crossover, with the subwoofer's outputs then routed to the inputs of the TS series speakers.
Your signal chain should be: Cabled Audio Source > Subwoofer Inputs; Subwoofer Outputs > TS Loudspeaker Inputs.
In this setup, the TS series loudspeakers function as receivers for the subwoofer. They cannot output Bluetooth audio back to the subwoofer.