Sad to say (largely due to how we need to authenticate players), it will not! But all itch.io game purchasers can redeem a Steam key: https://itch.io/t/67604/how-to-get-a-steam-key-from-your-itchio-purchase
That said, our current plan is to continue updating the itch.io version, just will not include the multiplayer section (similar to how Steam Workshop integration is hidden from the itch version).