Yeah. Especially because Amazon pays to retarget people based on their cart items until they convert. So if you have goods listed on Amazon, this is a way to quickly get people that you interact with on Twitter to sign up to get more pressure on them to make the extra step from add cart -> purchase. If they can make it so that you don't even have to visit the Amazon site to give you cart reminders I could see more people than just Amazon adopting this. So you effectively get free ads on Amazon's dime if you can get customers to adopt it.
Even people like small authors could do great with this: they can have a smooth transition from talking about their book with people online to having them buy it without relying on people's keeping their short term memory together so they remember to pick up the book. Authors sell books on their book tours because people don't have a chance to forget to pick up a copy.
If you find it annoying, you can just either not follow the Amazon accounts or block them. This is a nifty little thing, and it'd be a shame if it gets screwed up.