I don't know Power BI, but you can create a live connection in Desktop, then publish that to the Server and then the Server can directly access the database
Yes, with a couple of caveats.
1) You need to be on a recent release (2018.x). You can create a connection to a root data source from Tableau Server and publish it as a Tableau Data Source.
2) Not all connectors are supported (e.g., there are more connectors available in Tableau Desktop than in Tableau Server)
3) You have to have the right license level on Server to do this (Creator ONLY; Explorer and Viewer cannot create data sources on Server)