The Web Data Connector can be refreshed with the Tableau Server product.
Refresh the extract for a connector
When a user creates a workbook that uses a web data connector, Tableau creates an extract from the data returned by the connector. If the user then publishes the workbook, the publish process sends the workbook and the data extract to the server.
Tableau can refresh an extract that was created by a web data connector, the same as it can refresh any extract. Tableau Server cannot invoke a web data connector to refresh an extract if the connector requires credentials to sign in to the web-based data source. This is because the refresh can occur on a schedule or in some other background context, and the server cannot prompt for credentials.
If the background process that performs the refresh operation fails, it creates an alert and a log entry that indicates this issue. (Users will be able to see that the timestamp on the extract does not change.)
Source and additional information:Web Data Connectors in Tableau Server
I hope this helps!