Imagine that our sun suddenly collapsed into a 1-solar-mass black hole. What would happen to the orbits of the planets? Nothing. The black hole would still exert the same gravitational pull as the sun did. The same is true if you replace all the planets with equivalent-mass black holes.
Denser objects in an atmosphere or other fluid, where there is friction and buoyancy, will tend to sink to the bottom. However, if you're in the vacuum of space, there is no concept of "sinking". There is nothing to sink in unless you enter the atmosphere of a planet or star.
However, maybe there is enough interstellar dust near the center of the galaxy to produce a non-negligible amount of friction over millions or billions of years.
Mkay. I see my confusion. You need something like a fluid and also in a non-inertial reference frame which is under some force of gravity or acceleration. I guess a supermassive black hole such as Sagittarius A (assuming it exists) could provide a force of gravity. Then you'd need enough dust or something to exert pressure on the objects around it. It seems likely there's not enough of anything remotely like a fluid dispersed throughout the galaxy to have such an effect though who knows? I'm clearly no physicist :).
Denser objects in an atmosphere or other fluid, where there is friction and buoyancy, will tend to sink to the bottom. However, if you're in the vacuum of space, there is no concept of "sinking". There is nothing to sink in unless you enter the atmosphere of a planet or star.
However, maybe there is enough interstellar dust near the center of the galaxy to produce a non-negligible amount of friction over millions or billions of years.