You can restrict notification display on Android with several parameters such as disabling sound, vibration, or simply disabling notifications for that user if you have a way to ask for opt-in.
Batch Push provides you with an enum with the interactions a notification can have via: PushNotificationType. This enum contains ALERT, SOUND, LIGHTS and VIBRATE. By default, everything is activated.
You can call BatchPush.setAndroidNotificationTypes whenever you want in the runtime of your application.
BatchPush.setAndroidNotificationTypes(AndroidNotificationType.ALERT | AndroidNotificationType.VIBRATE | AndroidNotificationType.LIGHTS);
Please keep in mind that once you've set notification type within Batch, you have to set it again to change it.