If your TV has a headphone jack you can buy a 3.5 mm bluetooth transmitter
Probably not something you want to to considering the bluetooth audio delay anyway.
I think you can use an "audio out" device with the tv speakers at the same time. But how you turn the audio out to bluetooth is something I don't know.
Sorry I cant be more helpful'
editd to add this link from sony about speakers and bluetooth
I use a sound bar with my Sony Bravia and I can use both the sound bar and a Bluetooth device at the same time. The sound bar remote controls the volume at the TV and the TV remote controls the Bluetooth device volume. The echo is unbearable in the same room, but I can go inn the office and listen to a football game while my wife is watching in the other room.
Pretty good question but I don't think so.