I have set up SaA to use my Galaxy Active Watch 2 for measurements. The last couple of nights I did not wear my watch and my phone was sitting on the charger.
Sleep tracking started automatically and shows different sleep stages, too.
That might depend on your settings. There are different settings for how tracking starts and it can be set to start tracking automatically at your bed time. What sensor is your tracking configured to use? Sonar uses pings of sound to track movement, so that might be able to still sense your movement if it is close enough to you. I suppose it is also possible that it could pick up other unrelated movement our sound instead, too.