Have you ever used the stuff in the past? It should be plenty stiff for this application ;) I've made chairs out of corrugated cardboard - which is the same thing as coroplast except it's paper :D

Also keep in mind that you're fastening it to your under body - which will increase rigidity.

Personally, I think that it is stiff enough for the loads I would expect. Of course, I'm biased, because I have coroplast all over under my car, and would not want to admit I'm an idiot...