It's not really.Were orbiting the center of mass of the whole galaxy, Sagittarius A* just happens to be near there, but if it was to disappear not much would happen out this far.

Sagittarius A* is about 4 million solar masses, but there's possibly about 65 billion solar masses in other stars, then about a trillion solar masses or more in dark matter. We orbit around the center of mass of all of it, and so does the black hole which only makes up about 0.0004% of the total mass(though it could be located right at the barycenter?idk).