If I play Emperors Divide and it gets defied, does it still count for a 'choose' on Irelia?

Yes — Irelia, Fervent still gets +1 Might even if Emperor's Divide is countered by Defy.

Here's why: Emperor's Divide chooses specific units when it's placed on the chain (FAQ #7788, #8796), so Irelia's ability ("When you choose or ready me, give me +1 Might this turn") triggers immediately at that point. The trigger goes on the chain on top of the spell. Defy can counter Emperor's Divide, but it can't touch Irelia's triggered ability — that ability was already placed on the chain independently. When the chain resolves LIFO, Defy counters the spell, then Irelia's trigger resolves and she gains +1 Might for the turn.