Can Thrill of the Hunt instantly activate a Darius unit ability?

Yes, using Thrill of the Hunt to play Darius, Trifarian can activate his ability, provided that his entry onto the battlefield coincides with him being the second card played in your turn.

According to RiftJudge FAQs #10800, #10910, and #9495, playing a unit via a game effect (like Thrill of the Hunt) counts as "playing a card," and a card is considered fully "played" once it has resolved and entered the board. Because Darius is already on the board when his triggered ability checks for the "second card" condition, he can "see" himself as that second card.

The Sequence

1. Play Thrill of the Hunt: This is your first card played this turn.
2. Resolution: You banish a unit (which detaches any gear, per FAQ #10792).
3. Darius Enters: As part of the resolution of Thrill of the Hunt, you play Darius to a battlefield. He enters exhausted by default (Rule 811.1.c.3).
4. Trigger Check: Because Thrill of the Hunt was your first card, Darius entering the board now makes him the second card played this turn.
5. Ability Resolution: Darius’s triggered ability sees that he is the second card played. The ability is placed on the chain, and upon resolution, he gains +2 Might and readies himself.

Important Constraints

• The "Second Card" Rule: If you had already played another card (or cards) before casting Thrill of the Hunt, Darius would become the third (or later) card played, and his ability would not trigger.
• Token Exception: Tokens do not count toward the "second card" condition (FAQ #8290).
• Chain Timing: Remember that units played via Thrill of the Hunt enter the board before the "when you play" trigger check happens, which is why he is able to trigger his own arrival.