Vis-viva equation (Orbital Velocity) with massive satellite?

Wikipedia states that "In the vis-viva equation the mass m of the orbiting body (e.g., a spacecraft) is taken to be negligible in comparison to the mass M of the central body."

I'm wondering how the velocity is determined if the satellite's mass is non-negligible. For example, in a binary star system where both stars have comparable masses, would the vis-viva equation be accurate?

Thanks.