If I add cool whip to my cake and refridgerate it, will it get soggy?

I'm making my mom strawberry shortcake for mother's day. I'm going to bake the cake then ice it with cool whip. If I put the cool whip on it once its cooled, then refridgerate it till tomorrow, will the cool whip make the cake soggy? Or should I just put the whip cream on it before serving it?