If I equip Guardian Angel to Irelia does she get +1 Might from her effect?

Yes, equipping Guardian Angel to Irelia, Fervent triggers her ability and gives her +1 Might.

According to RiftJudge FAQ #9143, attaching gear to Irelia, Fervent is considered "choosing" or "targeting" her, which satisfies the condition of her ability: "When you choose or ready me, give me +1 Might this turn."