Short Answer: Yes there are power banks that can do that. However, the power bank must support the feature and your phone.A famous brand of power banks can support this feature is Anker one type can be found on Amazon. There are cheaper ones.
Output: However, this is strongly advised! First, being that you power bank will exponentially increase in heat depending on your phone. Second, the power bank will from now on take a double amount of time to charge up than not charging your phone at the same time. Third, depending on your phone it will take even longer to charge your phone even once you go back to an adapter and a outlet in the wall. Choose wisely.