A Dynamics AX 2012 R3 image is used in a training class where we can have 2-20 students. Normally we setup individual images each clones of the original and everyone has their own complete system. I am trying to figure out a way to build these student systems quicker but they all have the same login to the machine. Can I use Differencing Disks so that the original image is the parent and each student is a child? Will each student still be able to login as "Administrator" on their image as they would all be technically logging into an ERP that is originally on the Parent image?

Yes, but you'll need a lot of bandwidth for all the reads from the parent image's server.

What I'd do is copy the parent image to each of the students computers, write-protect it, and then create a local child off the local parent.  There'll be a significant increase in performance.  When that student is done, delete the child image and create a new one for the next student.