Chazarat HaShatz

Question

B'chvod HaRav, I have heard that if the Shatz does not say the entire Amidah outloud, than one is not yotzei the chazarat Hashatz. Specifically this situation arises during Modim. Usually the Shatz says the beginning of Modim and than completes the rest quietly to himself. My question is twofold - One... are you yoztei Chazarat HaShatz without the Modim being said outloud and two, if you are not yotzei do you continue to say Amen during the completion of the Chazarah. Thanks once again!