I had exactly this happen at Ballarat the other day. I was on final in a busy circuit with two 172 from the local training org (STATA) waiting to backtrack 18. I was more than a little surprised to see the lead AC enter and begin backtracking. I got on the radio and advised where I was, no response. Started getting a little irate and asked the AC intentions, no response. Landing light on, strobe on, another call - still no reply.
I suggested the pilot open their @*#^ eyes a bit and just then it lines up and blasts off, no call. Next thing one of the instructors gets on the radio and tells the student to get on the deck ASAP and report to HQ for reaming.
I got down without drama and plenty of margin but in hindsight I probably should have gone around but at the time I thought the safest place was behind the student than beside or in front of them.
Incidentally one of the school managers appeared when I was tying down and apologised which was unnecessary but good to see they keep and eye on things.
Scott