No, it's not safe to assume that--the backgrounder jobs do need access to the databases referenced by workbooks (for both Extract refreshes and Subscriptions). The Data Engine process itself does not.
But, my question would be, why do you ask? Are you trying to determine where you need to install drivers? Or are you trying to limit access by whitelisting certain hosts for your database servers? Generally speaking, I would want to ensure that all hosts have access to the database(s) and have all drivers installed, in case you need to re-arrange them for some reason.
i would second Matt on this. Usually in our environments, As best practice we install drivers on all the Servers to ensure that is consistant across the board. Also if you need to restrict access to Datasource, you can use Access controls at data source level instead of blacklisting tableau server IPs
You can see the processes that require database connectivity below:
Hello, thank you for the very good link, it answers my question. The reason I was asking not because of the drivers. I wanted to have a separation of layers where one node would be a "web server" that does not need any database connectivity and one or two "backend" nodes that do.