I have solved this problem, all you need to do is rename the file "C:/ProgramData/FAForever/bin/ForgedAlliance.exe" to SupremeCommander.exe, and create a symbolic link from this file e.g. using the LinkShellExtension tool to the name ForgedAlliance.exe
After that, if you run the game via FAForever, the binary file will be displayed in the task manager as SupremeCommander.exe (not ForgedAlliance.exe) and the audio will magically start working!