From my own experience of applying for anything on the Deutsche Bahn site, the status of 'Application in Process' is simply the application has been received and being considered. As long as it remains as this you are fine - keep your fingers crossed.
The one to watch out for is 'End of Process' - this is game over. Cross Country also have a habit of not informing people when they have not been successful - this has happened to me twice now. I've learned about my fate by logging on to my DB account and I have never had the 'unsuccessful' e-mail from XC.
Finally, I'm lead to believe the XC recruitment team is small so you might be in for the long haul playing the waiting game, as I've also experienced myself. Good luck with your application.
CJ