It seems like you can't prevent playing a sound on a channel to cut off a sound that is already playing on the same channel.
Example case:
Your minigun has a looping fire state where you want to play a looping firing sound, but only if the sound is not already being played on the channel.
using A_StartSound with CHANF_LOOPING (which means CHANF_LOOP and CHANF_NOSTOP), or just CHANF_NOSTOP, makes no difference; the sound already playing on the channel will always be cut off.
I constructed a simple showcase. Just load it with Doom.wad or Doom2.wad, summon the "Test" actor, and hear the shotgun sound being cut off by the pistol sound.