Only if the payment app ties directly to a bank account, rather than a card. I don't see any movement in that direction in the US, so the card networks would still be getting their cut.
I foresee a Wallmart/Amazon race between banks and online wallets in the future (each trying to become the other first). Paypal nearly got there a while back. They were actually paying more interest on your Paypal balance than banks were paying on your savings, since they didn't need all the infrastructure involved in being a bank. Not sure what happened to kill that.