Is the server address of SLSVR003.smasterandfaster.com really publicly accessible? That feels like an internal address only to me.
It requires username and password to verify. But I have embedded my credential in the data source. Shouldn't be an issue, right?
Is the ODBC driver different to the native driver? Like when you connect to data from the Tableau home screen, are you clicking 'MySql' or 'More' then 'Other ODBC'. If you are using the 'Other ODBC' option then I'm not surprised and no, it won't work. Tableau Online only supports live connections to a number of databases using the connectors outlined here - Tableau Online: Allow Direct Connections to SQL-based Data in the Cloud
If you are using the native 'MySQL' option then yes, it should work! If this is the case, I would create a support ticket with Tableau support so they can troubleshoot further.