Email - Updating the Custom SMTP after the fact

Our campus is looking to create customized outbound emails for the different ticketing apps now that we are exanding into more and more ticketing applications.  We did not configure this at implementation. A question was raised as to what happens if someone replies to a ticketing email from before the change is made? Does the content of their email reply still update the ticket? 

We currently have the default notify@teamdynamixapp address on all of our TDX email notificiations. If we set up the custom outbound settings to be something like "teamdynamix@delhi" will older tickets still get updates via email replies?

Thank you,

Holly