As previously mentioned, the Faraday pouch will block any type of incoming signal, including calls and text messages. With that being said, while your phone is in the bag, you will not be able to receive any calls and messages.
However, the phone is out of the bag, and it connects with the network, then you will receive the notifications that you missed. This works in the same way as when your phone is out of range and the caller isn’t able to contact you.