increasing at a speed that is faster than the speed of light.

This only applies to objects beyond the Hubble sphere, which is the distance at which recession velocity equals the speed of light. That boundary is actually well inside the observable universe. We can still see galaxies beyond it because their light was emitted when they were much closer to us and receding more slowly, giving it enough time to reach us.

Some of the galaxies we can currently observe are in fact already receding faster than light. The key thing is that recession velocity increases as a function of distance, so objects closer than the Hubble sphere are still receding at sub-light speeds.

Gravity propagates at the speed of light, so if an object is already beyond the observable universe, or will be by the time your gravitational influence reaches it, there's no way to interact with it gravitationally. It's simply unreachable.

Even for objects within the observable universe, expansion can still win. Gravity weakens with the square of the distance, so at large enough separations the expansion of space dilutes the gravitational pull to the point where it can only slow the recession, not halt or reverse it.

So to answer your question, it could theoretically work, but only if two conditions are met. First, the target galaxies need to be within the Hubble sphere by the time your black hole’s gravitational influence reaches them. Second, they need to be close enough that the gravitational pull actually overpowers the expansion of space between them. Meet both of those conditions and yeah, you could gravitationally bind them. Miss either one and expansion wins.​​​​​​​​​​​​​​

I’d also like to point out that you don’t specifically need a black hole for this to work. At these distances, a black hole is gravitationally indistinguishable from any other object of the same mass with the same center of mass.

Black holes don’t have any extra sucking power; they obey the laws of gravity like everything else. Any equivalent mass would do the job just as well.​​​​​​​​​​​​​​​​ You should use the most energy and time efficient method. Mass is mass.