Yes, but the OP asked a really straightforward question, and is it fair for us to overcomplicate the answer in a way that might cause confusion? I'd rather stick to the simple answer that adding a lens hood doesn't change exposure. Lens flare of different types can happen with or without a hood, depending on the particular shooting circumstances, but that's not a factor that changes the underlying general principle. After all, shielding the lens from oblique light with your hand can prevent flare too, but nobody in their right mind would suggest that having your hand somewhere near the lens but out of the frame affects exposure in general use.
So to make things clear for the OP: Adding a lens hood doesn't change exposure in the way mentioned in your original post.