If Darius Trifarian is played to the board from deck from Rek'Sai's legend ability after 2+ cards have already played, does he ready and get +2 from his effect?

No, Darius, Trifarian will not ready or gain +2 Might in this scenario.

According to the rules and FAQs regarding Darius, Trifarian:

1. Requirement: Darius triggers his ability only "When you play your second card in a turn." This means he must either be the second card played himself, or be on the board to "see" the second card being played.
2. Timing: If you have already played 2+ cards in the turn before resolving the ability from Void Burrower, the condition for his trigger ("playing your second card") has already passed.
3. No Retroactive Trigger: Playing Darius as the third (or later) card in the turn does not satisfy the condition. Because he was not on the board when the second card was played, and he himself is not the second card being played, his ability will not trigger.

Important Note: Even if you were playing Darius as the second card of the turn, the interaction with Void Burrower's ability works differently than playing a card from your hand. You are playing Darius from the top of your Main Deck via an ability, which still counts as playing a card, but he must specifically be the second card to trigger his effect.