Effectively yeah. See the sun is the center of mass and it's already moving. It orbits the galaxy in an up down motion along the spiral arms over thousands of years. We recently reached the middle point btw.So any movement we made would bring all the planets in the solar system with it, so long as we are careful in doing so?
But since something like 98 percent of the solar system's mass is in the sun. Wherever it goes everything else orbiting it follows. Save for maybe some remote ort cloud objects.
This would be far trickier if this was a multiple star system or the sun was a red dwarf or something simply because of the mass difference.