If you choose a unit with two spells, even if the spells are countered, can you trigger Ezreal's legend ability? Or would it not count because the spells do not take effect to choose?

Yes, you can still trigger your Ezreal legend ability in this scenario.

According to RiftJudge FAQ #9631, RiftJudge FAQ #8979, and RiftJudge FAQ #9463, the requirement for Ezreal’s legend ability is satisfied the moment you choose your targets and the spell is finalized on the chain, not when the spell successfully resolves.

Why it works

1. Finalization vs. Resolution: When you play a spell, you choose targets as part of the process of finalizing it on the chain. Even if the spell is later countered (e.g., by Defy), the act of choosing the target has already been completed and locked in.
2. Countering: Per Rule 425.1.b, a card that is countered is not considered to have been "played" for effects that require successful resolution (like Viktor, Innovator), but the "choosing/targeting" action has already occurred on the chain.
3. Requirement Satisfaction: Because Ezreal’s legend ability specifically requires that you have "chosen enemy units and/or gear... with spells," the condition is satisfied the moment the spell finalizes, regardless of whether the spell subsequently resolves or is cleared from the chain by a counter.

The Sequence

1. Playing the Spells: You play two spells, each targeting an enemy unit/gear.
2. Finalization: As each spell is finalized on the chain, the choice of target is locked in. This satisfies the "chosen" condition for Ezreal.
3. Reaction: Your opponent plays a counter (like Defy) to counter the spells.
4. Resolution: The counter resolves and removes the spells from the chain.
5. Activation: Because you have already completed the "choosing" actions, you may now exhaust your Ezreal legend to activate its ability and draw a card, provided you are in an Open State (the chain is empty and you have focus).

This is my interpretation based on established RiftJudge FAQs regarding targeting mechanics and counter interactions. No official rule chunk explicitly contradicts this behavior.