Earlier quoted context omitted.
I don't think so, and I'm actually happy that Amazon is blocking Google on this front. Amazon is always protective its customer data though. Their e-mails don't have details or invoices either.
I find this behavior pretty hostile. Every other online order I can track right from my email except for Amazon's. Facebook also does something similar with its 'so-and-so made a post's emails.
Instead I use an application called FindMyParcels which I register my packages and get push notifications for them. It's a one man operation and works pretty well for me, so I didn't get bothered by Amazon's decisions.
Neither of these two companies are angels, but when they compete instead of forming a bigger eye-of-sauron, it's a win in my book.