Short answer: No.
Medium: Yes but you will have to parse through the EmailMessage looking for text that will uniquely identify a template.
Long answer: Yes with a couple of conditions. You can't have the exact template twice with the only changes being in the merge fields UNLESS you can distinguish between the objects. You'd need to call a method that would parse the text looking for the unique template identifiers (you'll probably want methods to for each template). It's certainly possible but not the greatest. I can't recommend more without knowing your use case.