Go through the Managed Apps & Updates section in Mobile Device Management Protocol Reference guide.
an MDM server can provide configuration dictionaries to managed apps and can read response dictionaries from those apps. Apps can take advantage of this functionality to preconfigure themselves in a supervised environment, such as a classroom setting.
Go through the linked web-page. It is apparent that while it is possible to leverage MDM to configure an app but it will require support from the 3rd party app developer. An enterprise app created by the same company managing the device can program their app to be configured this way. Support for 3rd party app like Dropbox and OneDrive depends on how it was programmed by their development team.
It's recommended to get in touch with developer in app specific manner where this feature is required.