Well, I called
Amazon Wireless and found out that this won't work for me, because I want to use the phone for a different line than the one that is due for the upgrade, and Amazon said that you have to use the upgrade only on the line it is meant for and you can't switch. With Verizon you can use the upgrade on any line, even if it is not due yet for upgrade.
I also found out that within the first 30 days you have to return or exchange phone through Amazon, but after that you can go through Verizon, and basically you will have a dual contract with Amazon and Verizon for the first 6 months. It would be a good deal but since I won't be able to use the upgrade for the line that really needs the phone, I guess I'll have to go through Verizon.