Yes, you or a guest can join a live stream on StreamYard with just your audio. There are two ways to do this, depending on whether or not you want an image avatar to be visible in the stream.
Audio Only with an Avatar
To do this, turn off your camera by clicking "Stop cam." This will put you into the audio-only mode. From there, click the 3 dots in the top-right corner of your video feed, to change the avatar image that viewers see.
Your viewers and guest will see your avatar pulse when you speak.
Audio Only without an Avatar
If you'd prefer to join without an avatar on screen, you can also turn off those avatars entirely, and just be in the stream audio-only. To do that, head to Settings > General > Uncheck audio avatars. Now when you're added to the stream your viewers and guests can hear you, but they cannot see you at all.
You will see this message that says you are now in the stream with just your audio.