Yes.
The email provides a direct link to the Tracker Report in Salesforce, where you can view detailed migration logs (Salesforce login required). 
PS: View Drag, Drop & Upload Files to Amazon S3, a Salesforce AppExchange app for moving files from Salesforce to Amazon S3: https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3000000B5ZPqEAN