Does equipping a weapon to Irelia Fervent give her +1?

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

According to RiftJudge FAQ #6203 and #3079, equipping gear to Irelia counts as "choosing" her. Because her ability states, "When you choose or ready me, give me +1 Might this turn," the act of equipping gear triggers this bonus.

As noted in the FAQs:

• "Choose" in the context of Irelia's mechanics is equivalent to "target."
• Attaching gear is considered targeting/choosing, which satisfies the condition for her ability.