Ok they could would with a lot of extra effort.
Making jigs as part of the class?, it would be the whole class (I had the same idea it does not work) I had 7 kids 90 minutes a day for 45 days and each kid did 4 projects (see my other posts) with the time it takes to teach the cam/cad software and designing projects time runs out fast and if you had to tile everything bigger then a shoe box the kids would get nothing done.
As for the thinking any flat surface would work well, you run out of flat surfaces fast in a shop that has to be cleaned every 60-90 min.
How long would it take to cut a sheet of ply into cab parts with a handy bot and tiling? If it is over that 60-90 min if would not have the kids do it unless they have a free class after woods, and even with that they will be taking up space that the next class will need.
I'm not tring to be a downer on the handy bot but if I brought two into my classroom instead of one desktop my kid would look at me like I was crazy.

Soooo, save you money, wright some grants, reach out to your industrially park, keep your eye on the forum and buy the biggest bot you can afford.