there is zero possibility of retrieving a deleted workbook from the log files. Do you have a backup of your Tableau Server deployment? If you do, then can you do a restore to a dev environment? This is one possible way of doing it.
+1 to Jeff's idea - Logs do not contain workbooks or data sources. Best bet would be to restore a backup to Dev and grab the workbook from there. If you do not have a backup, here's how to help yourself out for the future: Server Backup and Maintenance Automation | Tableau Software