I haven't tried this particular model, I'd advise you not to risk it. It may work, but it's not a supported configuration, so you may run into weird problems. I tried this on another iMac for example, and while the older OS worked fine for running apps, that older version of OS X could not control the newer iMac's fans properly, so they were loud. That made it unusable on a desk. It's just a simple thing, but given that experience I would say what you're comtemplating is totally not worth the risk. And the fact that this is in an educational setting and Apple won't support it means that even if it did work, you'd better be prepared to do any troubleshooting yourself, and there's no guarantee what works today would still work after the next point update.
You'd be much better off looking for an Apple refurbished 2010 model. There are still lots available. e.g.:
Refurbished iMac 21.5-inch 3.06GHz Intel Core i3 processor
Originally released July 2010
21.5-inch LED-backlit glossy widescreen display
4GB memory
500GB hard drive
8x SuperDrive (DVD±R DL/DVD±RW/CD-RW)
ATI Radeon HD 4670 graphics with 256MB memory
Built-in iSight camera
$929