Can we publish and synchronize excel 2013 table as SharePoint list. I understand that using export to excel functionality and using data connection changes in the list gets reflected in the excel. But wanted to check is it possible the other way (changes made in excel to list)
Yes, You can do it.But for a two-way synchronization you have to download a free Add-In from Microsoft. With this tool you have to create a list in Excel, publish it to a SharePoint list and synchronize with it.
Once you install it, then you should now see under the Design tab a SharePoint section with a button called Publish and allow sync. Please follow the below blogs for complete step by step process. Connecting an Excel Sheet to SharePoint
Note: even this is 2007 add in but works in 2013. You may need to restart you PC after add-in installation.