On Android, Batch relies on Google's push protocol, Firebase Cloud Messaging (FCM), to deliver push notifications to your users.
This means you can send push notifications to any devices that have recent Google Play Services installed, no matter where the app was installed from (e.g. PlayStore, alternative store, standalone apk, etc).
For Huawei and Honor devices that do not include Google Play Services, Batch relies on Huawei Mobile Services (see how to integrate Batch with Huawei Mobile Services).
In-App messages will be fully functional, regardless of the app store used to install your app or of any Google Play Services issues.