Not to be that guy, but if these students are going to be using AutoCAD in the near future 90% of what they will be doing for the first bit will be copy and pasting any way.
I'm not sure how much of the process you control but have you considered changing the way you are testing? I really like @Alfred.NESWADBA suggestion. Or perhaps you could provide a starting dwg with 'hidden' dwg elements. Something like a text identifier with a ridiculously small font at a known location. or perhaps a block with hidden attributes with some sort of identification. This would allow you to find out who is copying and who is the source.
You could also try a testing method similar to the way the test for certification. The upshot of those kind of questions is that they focus on using the program and not necessarily creating a drawing. Below is a question in the style of a certification test;
"(NOTE: THIS NOT AN ACTUAL QUESTION NOR IS IT MEAN TO REPRESENT ANY QUESTION ON THE EXAM)
Given a drawing, draw a circle with a given start point 1 and the radius ending at another point 2. What is the distance from another point 3 to where line 4 intersects the circle. "

From CADnoob.com
So in the example above they are not returning a dwg but a measurement taken from a dwg that they had to create in class. Most of the time these types of question only needed simple geometry so it didn't take much time to draw. So other examples might be like inserting a block at a given point and then exploding that block and taking a measurement from a section of that block to another drawing element.
Past that you might be ale to see about developing a key logger type lisp so that they turn in their dwg with a command history or something along those lines.
CADnoob
