I just saw that the Bluetooth receiver has an optical output. This revises my statement. So it should be possible without reservations and surround sound effect.

Should be possible. As far as I know, you would need a multi-channel system for such a project to have "real" surround sound, which I don't think is possible via Bluetooth. However, the Logitech system can reproduce the stereo input coming from the Bluetooth receiver with a surround sound effect. To what extent this effect does justice to what one expects from a surround system, I cannot judge.