If a Darius is in base exhausted, will hiding a card at a battlefield ready him and give +2 might?

No, hiding a card does not ready Darius or give him +2 might.

According to Rule 737.1.c.2, hiding a card does not open a chain, and more importantly, hiding a card is not the same as playing a card (Rule 737.1.c.1).

Darius's ability triggers "When you play your second card in a turn." Since hiding a card is a Discretionary Action (Rule 408.2) and not a "play" action, it does not count toward the requirement of playing your second card. Therefore, Darius will remain exhausted in your base.