Let's say I set up a big workbook using MS SQL as my source. Later down the line I change my setup to MySQL. Is it possible to simply move my workbook/sheets to use the MySQL instead of the MS SQL?
Yes you can, you can create a new data source with the same data and structure form another source and then "Replace Data Source" from the "Data" menu.
Be aware that calculated fields are not copied automatically, but you can copy these manually to your new data source from the old data source.