It depends on the details of what you were trying to do. You cannot light the status indicator on the outlet which has gone off-line. But if you are saying you have a different device which acts as a status light for you, and it would still have power, then it may be doable.
If you have An iPhone, The following method is not available. But if you have an android phone, you can use a combination of two third-party paid apps, Tasker and SharpTools, to capture the push notification and then perform a smartthings-controlled action (such as turning on a status light).
@joshua_lyon , Who is the developer of sharptools, can say more. Here’s one of his posts on the method for that:
But again, it depends on the exact details of what you were trying to do. What device are you using for a status light?