@cmartin I would think the reminder would go out to Test Users. I would think that is the point of a test user is for instances like these.
If you PM your company name and the test user name, I can take a look. I'll also ask my colleagues and see what they say to confirm.
You can set email notification separately for 'Status Change Notification' and 'Sent Back Notification'.
Usually, for the sake of simplicity, these both are set with same default Status change notification, but if required, you can choose these differently.
This is part of 'Workflow' setup and applies to both Expense and Request module.
Incase if you wish to build an email reminder instead of email notification, you can do so but as the below fields are mandatory, your user will end up receiving 2 email no Sent back action.
If it is in Concur Test entity then as default the email server is turned off, you may request support to turn on for Testing if needed.
If the Test user is created in the Concur Production entity, then you should get an email. No problem with setting as Test user. You may check the Expese preference in the User profile to see if these are turned off by mistake.