Typically yes but it may depend on the particular TV audio output that is connected to the input of the TV adapter (streamer). For example, if you use the TV headphone output (if it has one) to connect to the streamer, that typically mutes the TV speakers.
In many TVs, the optical output has a signal at all times. In others, you may have to turn it on or set it to a particular output setting to correctly work with the optical input of a TV streamer (if it has such an input - not all do). In my case, Oticon recommends that the optical input for the streamer be used if available for a number of reasons so that is what I use as my (now old but flat screen) TV provides that and it is always on.
Depending on the details of the TV, any associated equipment like sound bar and the type of connection, and the streamer, others can probably hear the output of the TV and the streamer would provide you with a version of the TV audio via you hearing aids. One caveat, there is a possible latency in the audio signal as provided by streaming to your hearing aids or the audio system used by the others. If your hearing aid microphones are on when you are also streaming, you may hear two versions of the TV audio that are slightly different in time - that can be heard as an echo if the latency difference is large or just a smearing or change in timbre of the sound if the latency difference is fairly small.
In my case, I typically mute the hearing aid microphones if others are watching TV with me to reduce the effect even though the latency difference in my setup is probably quite small. For me, the streamed version of the TV audio is more easily understood and muting the microphones gives me better speech understanding than having both inputs. That said, most hearing aids combined with streamers have worse low frequency output than good audio systems (TVs with good audio and/or decent sound bars or amplifiers and speakers). I find the better voice understanding to be more valuable than booming bass.
