If it comes to your question, then I can answer yes - in our stages-driven approach, we need owner of each case and status of it. Both of them are updated at begin of every case.
At every step in application, we need someone to perform dedicated task (a current user, other specific user or work queue) and current status of it. We are able to control status assignment of each step in Designer Studio.
Did you tried already to set status in case management through "Set status" field?
In your case is necessary to use alternate stage instead of local action?