I wouldn't do it that way. A true torsion box will have a top and bottom skin to develop full strength and as John said at that scale the skins can be on the order of 1/4" thick. Nominal 1/4" lauan makes a nice light stiff box.
You can use breather fabric but I favor a separate grooved platen on top of the torsion box that both provides air evacuation channels and prevents my wood membrane frame from bending inward. The commercial aluminum extrusion frames are stiff enough to avoid that problem. You will need a good sealing surface on the top of your torsion box such as smooth plastic laminate or a good build of finish. You will be pulling a lot of air through unfinished mdf and your frame gasket needs a smooth surface to compress to.