Doubtful - Amazon is a huge customer, for sure, but FedEx and co regularly request that Amazon rely _less_ on their services during busy times of year. I'd bet Amazon has ended up at a point where they have been able to negotiate their rates with the other carriers so low based on their volume, that any additional volume isn't worth the cost of handling.
I worked for FedEx Ground HQ and that is basically how it works. Often UPS and FedEx trade high volume customers back and forth because they basically make no profit on them but it keeps the network full of packages. I think UPS, FedEx, and USPS handle my Amazon deliveries.
In my opinion it would be more likely for amazon to follow the SmartPost business, if they don't already do this. They would move packages between their hubs and rely on a 3rd party to do the delivery to the house. In the Smartpost network, FedEx would move the package to the closest hub and then hand it off to the USPS for home delivery.
Also, FedEx is tiny compared to UPS. I'd guess about 1/3 the size.
I think Amazon is already doing that smartpost approach. I've had a package shipped to a local amazon warehouse then sent off to usps for next day delivery. Now with Prime Now they just utilize those drivers.
