Do countered spells give Irelia Fervent +1?

Yes, Irelia, Fervent still receives the +1 Might bonus even if the spell targeting her is countered.

According to RiftJudge FAQ #636 and FAQ #5762 in the retrieved context:

• Trigger Timing: Irelia's ability triggers when she is chosen during the spell's finalization, which occurs before the opponent has the opportunity to counter the spell.
• Chain Resolution: Once the trigger condition is met, the ability is placed on the chain. Even if the original spell is subsequently countered, the triggered ability remains on the chain and will resolve normally.

Sequence of events:

1. A player plays a spell and chooses Irelia, Fervent as the target.
2. Irelia's ability triggers and is placed on the chain above the spell.
3. The opponent has the opportunity to play a "Counter" effect against the original spell.
4. If the spell is countered, it is moved to the Trash and does nothing.
5. Irelia's triggered ability, which is already on the chain, resolves, and she gains +1 Might.

This interaction is consistent with Rule 412.1.b, which states that a countered card is not considered to have been played, but it does not retroactively remove triggered abilities that were already placed on the chain as a result of the initial targeting.