The short answer to your question is simply no. But before providing further explanation, let me give you a high level description of how the dispatching of these emails works.
Basically, for each action that a retailer performs at the Point of Sales (POS) on a given order, there are potentially 4 emails that can be sent to the customer: the thank you email triggered when the order is downloaded at the POS, the fulfilled or shipping email which fires off when the order is tendered, the refund email triggered when the order is refunded at the POS. To know the exact number of mails that Sync can send, you should click on the File menu and Rescan Mail Template, Sync will inform you how many emails it supports. It does so by scanning the Mail Template folder searching for the following files: processed.xml, refund.xml, thankyou.xml
It’s worth noting that Sync on its own cannot directly dispatch any of these emails to your customers as it doesn’t have any access to the Mail Server. What Sync does instead, is to add an entry for each email to be sent to the Mailer table. To send these emails, Sync creates a child process for that. The pseudocode associated to that process is basically as follows:
1 - Scan the mailer table and locate any mail that hasn’t been already sent;
2 - For each email, send a request to the store and include the body of the mail in the request;
3 - Wait until you get a reply from the store and update the mailer template accordingly;
4 - Depending on the response, send the return code to the parent process (in this case Sync) and die.
At this stage, this is what will happen. At the store, when these requests are received unless the corresponding orders are regular ones, no email is dispatched to the customer. In fact, if you run Sync in the debug mode, you can see not only the process ID that Windows assigned to it but also the response text sent by the store to Sync.
Finally, you have a look at this thread, you will notice that the retailer is confirming that those emails are no longer being sent. Amazon Email not coming through
The best way to double check that for you would be to enable the Mail Integration and search your email for mails sent to your customers.
I hope this message has cleared your queries. Let me know if you have any other questions.