Hey Doug -
The "Parallel Queries" feature of Tableau is associated with the VizQL component of Tableau, not the Backgrounder. That's why Tableau Desktop (which doesn't even have / use a backgrounder) can take advantage of it.
When a dashboard is rendered (by the VizQL component), it can execute up to <x> queries in parallel.
The Backgrounder, on the other hand works on one thing at a time.
I thought I would update this thread, Tableau Server can have schedules for subscriptions or extracts run in parallel if other backgrounder processes are available.
This can be seen in the following online help document: