The answer

Missing call of abs()

Originally I did not have an abs() on meaning that it was setting the the shortest duration to a negative, causing errors further down. @IgorTandetnik pointed this out.

Old

for(int i=0; i < length; i++) {
    if(abs(durations[i]) < shortestDuration) {
      shortestDuration = durations[i];
    }
  }

New

for(int i=0; i < length; i++) {
    if(abs(durations[i]) < shortestDuration) {
      shortestDuration = abs(durations[i]); <-- This part
    }
  }

Comparison Issues

The adding the abs() call, fixed most problems put I did not handle the remaining value properly. It would be more robust with using the median and should do the timing thresholds outside the for loop.

Old

for(int i=0; i < length; i++) {
    if(durations[i] > shortestDuration * (1 - Variability) && durations[i] < shortestDuration * (1 + Variability)) {
      Serial.print(".");
    } else if(durations[i] > shortestDuration * (3 - Variability) && durations[i] < shortestDuration * (3 + Variability)) {
      Serial.print("-");
    } else if(abs(durations[i]) > shortestDuration * (3 - Variability) && abs(durations[i]) < shortestDuration * (3 + Variability)) {
      Serial.print("/");
    } else if(abs(durations[i]) > shortestDuration * (7 - Variability) && abs(durations[i]) < shortestDuration * (7 + Variability)) {
      Serial.print(" ");
    } else { // <-- This does not handle the interspace between morse characters
      Serial.println("miss");
    }
  }

So then I changed it, with the help of @IgorTandetnik. So that it properly handles the interspace between characters and so the variability scales well.

New

for(int i=0; i < length; i++) {
    if(durations[i] > shortestDuration * (1 - Variability) && durations[i] < shortestDuration * (1 + Variability)) {
      result += ".";
    } else if(durations[i] > shortestDuration * (1 - Variability)*3 && durations[i] < shortestDuration * (1 + Variability)*3) {
      result += "-";
    } else if(abs(durations[i]) > shortestDuration * (1 - Variability) && abs(durations[i]) < shortestDuration * (1 + Variability)) {
      ; // <-- This does
    } else if(abs(durations[i]) > shortestDuration * (1 - Variability)*3 && abs(durations[i]) < shortestDuration * (1 + Variability)*3) {
      result += "/";
    } else if(abs(durations[i]) > shortestDuration * (1 - Variability)*7 && abs(durations[i]) < shortestDuration * (1 + Variability)*7) {
      result += " ";
    } else {
      Serial.println("Duration to morse Error");
    }
  }

Timing

I also had a slight timing issue with random, where originally I did random(0,1) which meant that it only returned 0 as it (max - 1) which returned 0, so changing to random(2) fixes this.

Old

void addNoise(int* array, int length, float fraction) {
  for(int i=0; i < length; i++) {
    long variability = random(fraction * 100);
    long plusMinus = random(0,1);
    if(plusMinus == 0) {
      array[i] = array[i] + variability ;
    } else if(plusMinus == 1) {
      array[i] = array[i] - variability;
    }
  }
}

New

void addNoise(int* array, int length, float fraction) {
  for(int i=0; i < length; i++) {
    long variability = random(fraction * 100);
    long plusMinus = random(0,1);
    if(plusMinus == 0) {
      array[i] = array[i] + variability ;
    } else if(plusMinus == 1) {
      array[i] = array[i] - variability;
    }
  }
}