I'd guess they'll be elated. Delivering packages in the far reaches of suburbia (and beyond) is probably costing them money, as it takes a lot of truck&driver time to deliver a single package. If we assume they maintain their hold on urban deliveries and let amazon take care of the suburbia ones; their margin will go up.

Also, I'll point out that in my area of suburbia, UPS/Fedex sometimes deliver to USPS and let USPS do the last mile. it's not hard to imagine they'd deliver to an amazon base station where robots & drones would take over.