Heuristics say that feedback should be provided when:
- Fits importance and urgency
- Comprehensible and meaningful
- Within appropriate context (time and place)
I don't know if there is any research on this. I can say that personally I have never considered relevant status updates for my order to be flood or overwhelming and I find it important to be informed on the go instead of me logging in on the website to find out what the status is.
The store I make most of my purchases will notify me with:
Thank you for buying X it will be delivered on xx/xx
The package was shipped
The shipping will be delivered today between x - x hours
Yet it would be cool to get another notification that the van is in my street so I can make sure I am able to open the door to receive the delivery.