V-Play and Qt package all libraries that *might* be needed as a dependency at runtime. If you’re sure that some modules are not required at all by your app, you can overwrite the included files with the ANDROID_DEPLOYMENT_DEPENDENCIES variable, as described here: http://doc.qt.io/qt-5/deployment-android.html#android-specific-qmake-variables and save some MBs in file size. There also come quite some examples up when googling for that variable.
In case the APK size is a major issue for you and you can’t manage to accomplish it on your own:
We offer to build a stripped-down version of the V-Play library to remove modules you might not need. This can also save a few MB depending on your use-case. We can create such custom builds with the purchase of a support package or the included support of the V-Play Enterprise plan.
an estimation beforehand is really hard as many factors affect the APK size. For example, last years Qt World Summit app in Google Play is listed with 38 MB.It includes assets (images, …) that take up roughly 12 MB (uncompressed). Without any assets your app will probably use between 20 and 30 MB, depending on
the linked Qt Modules (as said above, a few MB can be saved by removing ones you do not require, this is possible with custom V-Play builds for Enterprise Customers)
linked 3rd party Frameworks, e.g. of the V-Play Plugins your app is using, or for custom features (like the QZXing Barcode Scanning library used in the Qt World Summit demo)
amount/size of your source code (usually the smallest factor).