. . . and have my students open it in their Student versions of ExtendSim?

No, but there is a work-around.

The Student version of ExtendSim can open models built in or shipped with ExtendSim Student or in an activated Model Developer Edition of the software, but cannot open models built and saved in a Trial version.

So, if you build a model in a Trial version of ExtendSim, purchase and activate that license, then re-save the model in the activated license so it can be opened in a Student version.