While I don't know if you'll run into complications because the data is on sharepoint, the utility you're looking for is the Tableau Data Extract Command-Line Utility. You can script the extract refresh on the machine with Tableau Desktop then use a scheduler to refresh when you want.
I hope this helps,
I thought this can only be paired with Tableau Server, no?
Yes, OData extract refreshes are possible - you have any issues with it?