I think it depends on the state you are in. In WI, we can check the status of our application on the BOP website and it will list each part of the application that has been completed. It'll list "passed" in the MPJE or NAPLEX section (even if you've only taken one exam) usually a day or 2 before you get the results in the mail.
From my understanding, some states are not like this. Sounds like a few will hold the results until both tests are completed. That would drive me nuts...