I believe it's still theoretically possible because brown dwarf is much more massive than 3I/ATLAS. During initial gravitation pull a smaller body can be accelerated to much higher speed than bigger object speed, and then thrown like a slingshot.3I/Atlas is much faster than the solar system escape speed (60,000 km/h). All the planets and the brown dwarf are way below that or they would not stay in an orbit around the Sun.
The orbital parameters of the brown dwarf, which the C's gave, indicate a maximum speed of about 6 km/s (20,000 km/h) at its closest approach and about 2 km/s (7000 km/h) currently.