Does Irelia "Blade Dancer" can still be used if the chain where I chose a unit already ended?

No — once that chain has finished resolving and cleared, the window has closed.

Blade Dancer is a triggered ability that goes on the chain as a Pending Item at the moment you choose the friendly unit (CR 383.3), which happens during finalization of whatever caused the choice — playing the card, activating the ability, equipping the gear. If you decline to trigger it there, you can't add it afterwards; the chain isn't a state you can reach back into (FAQ #11317).

It isn't a once-per-turn ability, though, so the next time you choose a friendly unit — equipping gear, playing En Garde, etc. — you get a fresh trigger and can pay the [A] to ready.