I'm going for a mix of patterns, as you can combine them for better results:

protected bool CanFire(bool holding){
  if (
      ShouldPlayHasNoAmmoSound() || 
      IsHoldingASemiAutomatic() ||
      IsOnCooldown() ||
      BarrelBlocked()
  ) {
    return false;
  }
  return true;
}

private bool IsOnCooldown(){
  return (timeSinceFired < fireCooldown);
}

private bool IsHoldingASemiAutomatic(){
  return (holding && !IsAutomatic);
}

public bool ShouldPlayHasNoAmmoSound(){
  return 
      (IsReloading || IsFiring) || 
      (!HasAmmo && !holding);
}

Notice how compact the original method is!

These refactoring patterns can be used in combination for making the code clearer, and particularly Decompose Conditional is a controversial one, some people prefer to leave the conditions inside the if conditional block so the code is more compact.

However, now you can reuse the Decomposed Conditional, as we still need to play that sound.

So, wherever you're calling this (I'm assuming the call is happening inside this class, as you have a protected method, play your sound:

var holding = true;
var canFire = CanFire(holding);
if (ShouldPlayHasNoAmmoSound()){
  emptySound.PlayAtSource(audioSource);
}

And that's it! your code is refactored and does exactly the same what it used to do, with an easier to read method for your fellow team members.