When the End User completed his/her design, what format is the output file received in on the backend system in WooCommerce?
It's saved in the Database. Files are only generated once you use the order viewer (output files can be .png, .jpg, .svg, .pdf)
Can the output file be stored in a layered pdf format that can be imported to Illustrator with the corresponding layer configuration so that the layers can be enhanced edited, etc...?
Yes, if you save it as .pdf with the .svg image format.