Polyethylene is generally a semi flexible plastic. It's used in the construction of everything from milk cartons to kayaks.
Even with wall thicknesses of up to 1/4", I've had kayaks where you could put dents in the material. Yes, the dent pops right back out, but it's far from a 'rigid' surface.
Worse yet, bonding Polyethylene is
very difficult. Basically, when you get a crack or gouge in a kayak, you have to 'weld' it back together using highly focused heat and additional poly sticks. I'm not even sure high grade silicone sealant/adhesives will stick to it. I've never tried using construction contact adhesive like Liquid Nails, but my guess is it wouldn't hold; the moment the material flexed, the adhesion would crack and release.
Since the majority of our 'torsion box' effect comes from a solid bond on all perimeter seams, I'm not sure you could get the same level of rigidity out of the torsion box since you'd, at best, only be able to fasten screws into your framing ever few inches. And even then, without a way to properly seal the screw holes and window/door/vent openings, water intrusion is probably inevitable.
E.