I bet the Dalite material would make an outstanding DIY screen. But I guess I don't see a need for any backing "board" if you just stretch the fabric over your own frame or artists' stretcher bars and staple or nail it off or even use the porch screen runners I've seen suggested here. I suspect your average multiplex screen is stretched across a frame of some sort w/o any backing board. The drywall would be pretty heavy to boot, and you'd run the risk of whatever adhesive you use delaminating from the backing and forming ridges or bubbles, etc.
Unless you get a downright steal on the Dalite material, you may wanna consider some of the other DIY screen fabric options that have been discussed on this board... window blackout material, artists' canvas, painter's dropcloths, roll-up shades, etc. Just do a search for "DIY" or something and see where it leads.
I'm too am wanting to "roll my own" screen here soon and am currently investigating all of my screen fabric and construction options. Looks like it will be a fun quest.
Good luck and let us know how it goes,