can i use irelia blade dancer when i equip a gear to a unit?

Yes. Equipping gear to a friendly unit counts as choosing that unit, so Blade Dancer triggers — you may exhaust Irelia and pay [A] to ready the equipped unit (Equip's choice is a Target, Rule 818.1.b.1).

One catch: you can't ready a unit that's already ready, so this is most useful if the equipped unit is exhausted (Rule 415.1.b). The trigger resolves on the Chain, so if the unit is exhausted it gets readied after the Equip ability resolves.