I think in the long term you can expect to see Amazon directly competing with other carriers in retail parcel delivery, so yes.
However, the carriers have a very difficult job, and contrary to popular belief, they are phenomenally cost efficient given the constraints placed on them. Amazon may try to undercut on price, but given the cash flows and margins of large carriers, any significant pricing discount would introduce negative cash flows that could cripple even a behemoth like Amazon. And by significant, I mean anything more than 2-3% off of the rates that UPS or FedEx charges.
Given the constraints and inherent difficulty of the business, I would imagine the impact would be no different than if DHL tried to re-enter the US market.