Should I be able to open up the Serial Monitor on any Arduino sketch that I've uploaded successfully as long as the Serial.begin (9600); is at the start of the void setup ? And if nothing comes up on the Serial monitor screen, does it mean there could be a fault in the sketch ?
No, because if you only call Serial.begin() nothing is send. You also have to write something to serial to see something on the Serial monitor. Also, baud rates have to match.