There are multiple types of brands out there so let's just talk about Autofoam. Then it hardens it becomes pretty strong therefore if it was pumped into the sills, hollow chassis "bones", pillars etc - it'll expand and stiffen the usually hollw metal beams or whatever. Technically it should stiffen the whole frame and reduce "echo" or dampen sound. So yeah, it should reduce NVH and stiffen the car overall. But there's a caveat too - even Autofoam has 2 or 3 types of foam. The "race spec" one is the one you'd want to go for if the car needs to be solid stiff. The 'weaker' foam is stiff still but less.Well what about chassis foaming ? Do those help besides NVH. I see alot of cars like to cover their bottom with those.
It's all about trial and error if you ask me. I've tried both the cheap brands and the premium Autofoam brand and seriously don't bother with the cheap one.