Hi,
I have an interest in education, I make a living working with large scale LED screens.
It's a nice idea but not really that suitable for you. Most of the LED curtains that you see on major concert productions are relatively low resolution screens (measured in pixel pitch, generally 15mm or higher). To get a useable picture for watching films or presentations on a small screen (<20sqm) you would need to be looking at 10mm actual pixel pitch or less. That would become expensive. I can't really tell you prices, I put the things up and make them work, I don't sell them but for a rough idea 3.5sqm of 20mm curtain is going to be around £8000 and that would be half the resolution you need for it to be any real use.
They can be a nightmare to maintain. If they're a cheap import you will struggle to get support for them after a very short time.
You would be much better off with a good quality, high output projector. The resolution will be better and the price considerably lower. If you need a proper blackout during your show then google 'projector blackout shutter' and you will find several simple but elegant solutions.
My big recommendation for any new arts space would be to make sure you have cat5e cables everywhere. You can't have too many runs and it is cheap. You can use it for all sorts of different signals; audio, video, networking. Increasing numbers of digital audio desks use cat5 to link their control surface to stage instead of big heavy multicore runs.
Hope this helps,
Peter