I would not use plywood for the torsion box slats. A torsion box design is based on good glue contact with the slats. Plywood just don't cut it on end grain. MDF will, but much heavier.
I would use at least 1/2 ply for the faces although I never used less that 3/4". The box itself will be heavy if you consider 3/4 ply weighing in at around 70 lbs per sheet and 3/4 MDF coming in at around 90 lbs per sheet. the torsion box will remain stiff regardless of the what it is resting on. Any irregular corners could poke through 1/4" ply for sure.
Tony B Retired woodworker, among other things.
"Strive for excellence and settle for completion" Tony B