This would work exactly the same way a signed document is mapped into the AssureSign object in Salesforce when an envelope is complete. It would just also put the completion report in there as well.
Right now you would have to manually go into AssureSign and download and then upload the completion report into Salesforce Files. If this was a feature and followed the same logic as a completed signed document then when a document is completed you would have everything you need in Salesforce.
I suggest this be optional because not everyone would want this file using up more Salesforce storage space which can be expensive.