I autofoamed my previous ride, the Civic FD1 and it did reduced the NVH of the car. If you ever driven one before, you'd realize how bare these Civics are, in terms of noise insulation. Anyways, to answer your question, it is not gonna improve the handling significantly, unlike changing an absorber or adding a strut bar. Here's the thing, the F10 is build for speed and handling so I'm pretty sure the chasis does not require further strengthening.
I would not auto foam the car for handling improvement purpose, but for NVH reasons, maybe yes.