With the distances we are looking at here, line of sight is not a problem. A object blocking the waves would create a wave-shadow.
Waves "enter" wave-shadows and at a given distance, which is calculated using wavelength and wave speed, after the border of the shadow, they will have fromed a complete wavefront again. This is in part, why we can have few signal towers IRL with a lot of recievers (actually there are a lot of reasons for that, but this is one of em). Additionally, as you pointed out with the black holes, Gravity of stellar objects helps the waves curve into the shadow even faster, thereby closing the gap to form a complete wavefront again. Of course you are loosing energy every time you have to close a gap, but we can assume that energy was not a concern for them. If all that even applies to FTL travel of waves, I cannot say, but theoretically it should. Especially when using extremely low frequencies (they were used for submarine comms, as they could bounce between the athmosphere and the gound better and lost less energy in the process, so they could even pierce water), which close the shadows faster (in less distance after the object that caused it) than their higher frequency counterparts, communication without line of sight is perfectly possible.