If I use Sacrifice on my Ekko Recurrent, and my opponent uses Defy to counter, does Ekko still die?

Yes, your Ekko, Recurrent still dies.

According to RiftJudge FAQ #10480 and Rule 357, the process of playing a spell includes paying its costs before the spell is added to the chain and becomes eligible to be countered.

The Sequence:

1. Announcement: You announce you are playing Sacrifice.
2. Payment of Costs: You pay the energy cost and the additional cost: killing a friendly Mighty unit (your Ekko, Recurrent). This happens instantly when you play the card.
3. Finalization: Only after your Ekko is killed and sent to the trash is Sacrifice finalized and placed on the chain.
4. Reaction: Your opponent plays Defy to counter Sacrifice.

The Result:

Because your Ekko was already killed as a cost to play the spell, it is already in the trash by the time Defy is even played. Rule 425.1.c confirms that countering a card does not refund any costs paid to play it, including additional costs. Your Ekko remains in the trash, and your Sacrifice is removed from the chain.