Hi Nathan,
That sound like a particularly bad idea for several reason; the first is that in the real world I’ve never actually encountered such a vehicle, so the audience consciously or sub consciously might wonder what’s going on. Of course if your project has a setting in the future or is a science fiction story where this peculiar truck bed setting would enhance the effect I’d retract my criticism.
If you never see the roof, it might work to construct the sides with darker canvas cloth, such as you might find used in such a truck and make the roof out of silk to allow in the soft diffused light you correctly seek. It would not be inexpensive to manufacture such a set. This is typical in many box trucks that have a white frosted plastic roof to illuminate the interior during the day.
From a lighting point of view, staging the action essentially in a white tent would be problematical, unless of course you want the actors to appear in silhouette. Is the covering complete including the back entry way or is that open to the daylight to allow a light source to enter? Is all the action in the daytime and/or at night? Obviously this would affect the type and quality of the light?
Also from a logistic point-of-view is the truck actually driving down the road as you shoot or being shaken to simulate travel. The lighting on the outside of the truck can indicate movement and or locale.
You might watch a movie that was just released where the whole film takes place in a closed trunk of a car. It was shot by James Mather the founder of the Digital Cinema Society.
Needless to say to do this convincingly will require considerable thought, planning and skilled execution.
Good luck,
JS