That really depends what your application does, the version of Android running on MC40 is AOSP only so if you are using any GMS libraries such as location services, FCM or maps then your application would need modification. If you are not using any GMS libraries then it would 'just work'.
EMDK for Android is a Java SDK to allow you to take advantage of your device hardware, for example if your application currently scans using the camera you could use EMDK for Android to scan via the MC40's dedicated imager scanner.
It is only possible to download Android Apps from the Play Store on GMS devices. Zebra do have a range of GMS devices in our portfolio but unfortunately the MC40 is not one of them.