No, it can't.
Enchant cards are put in the abyss or power charger at the end of the turn depending on whether they have SEND TO POWER. So an enchant card set this turn goes to the abyss at the end of the turn, and can't be chosen with Kitte-men • Inc-neko (Seigi).
However, if a different enchant card was already in the abyss from an earlier turn, you can choose it with Kitte-men • Inc-neko (Seigi), and together with the card in the set zone, use that enchant card's effect twice.