Maybe, but I can't think of how a cockpit mounted cage could possibly negatively affect crumple zones that are meant to keep the cockpit intact. It might make an accident a little more jarring from the extra strength, and less supple chassis, but I can't buy that it won't help protect the driver and passenger less than without a cage.

 

I read somewhere a long time ago that Infiniti used foam in the chassis of some of their higher-end cars for this purpose. Is this foam too pliable to be effective as a core?

 

I'm not sure about Infiniti's factory chassis foam, but I know most NVH reduction foam is somewhat pliable in order to be absorptive to noise and vibration. A foam that is rigid enough to work well as a core is usually too rigid to effectively damp anything. The higher the compressive strength of a core, the better it works because the more effectively it transfers loads from the core to the skins (in this case the sheet steel box section). Too rigid though, and when the chassis flexes there are enormous shear loads between the core and skins, and you run into serious core failure (breakage/crushing) or delamination. You can also run into problems with cyclic fatigue where the bond between the core and the skins will fail through repeated flexing. Boat hull cores sometimes have bad problems with this through flexing, temperature cycling, and pounding waves. Same problems, different vehicle.