A barycenter of a galaxy is the "balancing point" of it where every object inside the galaxy orbits. With this information, if somehow (I don't know how, maybe you can give me a way in your answer) some mass was added to one place inside the galaxy, then it would change the barycenter. If the barycenter changed would that throw of the orbits of stars or even change there orbits in any way? Why don't planets and moons and stars all have barycenters and orbit a black hole? Why do moons orbit planets, planets orbit stars, and stars orbit black holes? Why doesn't all the mass in the universe just orbit a common barycenter, like near a super-massive black hole?
If we introduce mass into a galaxy by any means such as coalescing of a cloud of matter into a concentrated mass, same feat that happened to a nebula's scattered gases and dust that turned into our solar system and sun, the barycenter will change.
Even if we don't add mass, the orbit of the stars of galaxy will move them to a different configuration at anytime, sometimes affecting the swirl of cloud of gases, sometimes not, and drag the barycenter along with it in a complicated curve.
Some stars of a galaxy will turn into a supernova and go through the process of death by losing much of their mass by radiation, hence effecting the location of barycenter.