I have done a video production of a board meeting with a mic on a table stand between every two board members for about 6 mics total.

It definitely required a human mixer who would use predictions to put some mic faders at a third if they are not likely to speak, other mics over a half if they were likely to speak and whatever mics were actually in use turned up to unity gain.

It was quite a process to set up requiring perhaps a person hour of time minimum for setup and breakdown.

Instead if I were in your shoes I would just have the students pass around a handheld mic and have the instructor make them use it. In such a small classroom that would be quick enough and in a semester class they would be old pros soon. Most importantly that saves the need for a lot of gear, and makes setup much easier. You could probably even get away with just using limiting and a well designed gain structure to avoid having anyone ride levels. Much more easily since it will be used close to the lips so you start out with a clean signal.