If you want that notifications for tickets coming on MailboxAddress to also have the From address be MailboxAddress it's a bit more complicated, since the notification must read what is the original email address (from the ticket). It can be done, I'd use the following method:
1. Use a custom attribute on the Incident (or any of the extra stringX unused Incident attributes) to store the mailbox address. This can be done in the Mailbox Rule(s) where you create the ticket, by using the TextAPI defaults configuration in the Rule
2. Create a custom notification method to replace the default Email method and execute a script instead of pdm_mail. - see Modify Notification Methods - CA Service Management - 14.1 - CA Technologies Documentation . In the script, read the file produced by the notification process and find the value of the custom/stringX attribute used to store the email address on the ticket. Depending on the value of it, execute pdm_mail -F<address_stored_on_ticket> (when you have a value stored) or directly pdm_mail (when the ticket was not created by Email).
3. Profit !
But without a staging/dev env, it's going to be a little trickier. You can start by creating the mailbox rule, defining the notification method and then use Manual Notify to be able to choose this new Notification method before replacing the default (Email) notification for all contacts.