Is a swimming pool analogy to building of black holes in the centers of galaxies valid?
The process of an eddy gathering matter to the centre of a pool is due to the motion of water in a vortex. Roughly, if water is rotating  counterclockwise then a secondary motion will be set up, rotating clockwise about an axis parallel with the tangential motion of the water. This tends to push debris towards the centre of the vortex. (The same effect causes deposition on the inside of meanders)

Space time doesn't work like this. There is very little spinning of spacetime around a galaxy, the amount of frame dragging is very small. And spacetime doesn't follow the Navier–Stokes equations, so there is no true vortex. The debris flows with the water, where as matter travels through spacetime. Your pool has a clearly defined "up", the galaxy doesn't. 

So while the appearance is somewhat similar, the mechanism is different. Though we don't really understand the mechanism of formation and growth of supermassive black holes.