eBay Module: Will my Store Send Email Notifications to eBay Users if They Purchase eProducts?

Unfortunately, no. As part of the eBay integration, there are guidelines set in place that Shift4Shop must adhere to. One such guideline is a restriction that will not allow their customers to be emailed from a 3rd party service (i.e., your Shift4Shop store) when the originating order was placed on eBay.

For your Shift4Shop store eProducts purchased on eBay, you must use the eBay interface to send those customers their eProduct download links.