You need the completion letter to determine kung anong date ng completion mo and to make sure that that date comes before your date of lodgement. If mag-lodge ka without it, and then lumabas ang completion letter mo, and yung date ng completion is after the date of lodgement, 100% refused yan. That will severely limit your options to stay in Australia. So worth it na mangulit sa school na i-expedite nila yab. After lumabas ng results ng final exams mo, kulitin mo na agad. Explain mo situation mo na kailangan mo for visa purposes.
Not sure school mo pero sa school ko, nalakagay yung date ng completion ko sa transcript. Though mas matagal lumabas yung transcript ko kesa sa completion letter, which took a day after ko mag-request.