You always ask the most the most perspicacious questions!
This is not a recommended practice since TD's cumulative experience tells us that this will cause more confusion than anything. We do not recommend this for similar reasons as to why the SB does not deliver scheduled reports, SLA violations, etc. Here is a KB that explains more about the different types of environments.
With that said, it is technically possible. However, you will need a different instance of the email service installed somewhere that points to the sandbox URL (SBTDWebAPI). You would also need different email in-boxes to handle the replies. Meaning, an inbox for prod (tdreplies@[domain].edu), and one for the SB (tdrepliessb@[domain].edu).
It is important to note that the user credentials that are used to authenticate into the environments from both instances of the email service can be the same. This is helpful since the data in SB gets overwritten with prod data every quarter, so managing the user credentials is made easy if its a user in prod.
But again, we recommend that this not be implemented.