Speaking generally, yes. Consider just the three body system of the Sun, Didymos, and Dimorphos. Despite the huge difference in their masses, Didy and Dimo revolve about their mutual barycenter – like the Earth and Moon, or Pluto and Charon, or even the Sun and the planets. This barycenter follows an elliptical orbit around the Sun.

Perturbing Dimo's orbit, by changing its mass, and its average distance from and period around Didy also changed the barycenter of the system. Therefore the impact on Dimorphos did change the heliocentric orbit of the Didy-Dimo pair. But in the real multi-body universe, the extent of this change is infinitesimally tiny compared to all the other forces constantly tugging on the Didy-Dimo system.