DB File in Assets Folder. Will it be Updated?

You can’t replace database in onUpgrade() because in this method the database is already in use. You have to do it before the database is open, like in a constructor of your DatabaseHelper. As you can’t use onUpgrade(), you have to manage database versioning by yourself. Using SharedPreferences is a good way for it. You check if your database exists (if it is already copied from assets directory) and check the version if database exists. Now you can delete old database and copy new one from assets.
See implementation below.

To mark your updated application is published with new database in assets just incerment DATABASE_VERSION constant.

private static class DatabaseHelper extends SQLiteOpenHelper {

    private static final String DATABASE_NAME = "database.db";
    private static final int DATABASE_VERSION = 1;
    private static final String SP_KEY_DB_VER = "db_ver";
    private final Context mContext;

    public DatabaseHelper(Context context) {
        super(context, DATABASE_NAME, null, DATABASE_VERSION);
        mContext = context;
        initialize();
    }

    /**
     * Initializes database. Creates database if doesn't exist.
     */
    private void initialize() {
        if (databaseExists()) {
            SharedPreferences prefs = PreferenceManager
                    .getDefaultSharedPreferences(mContext);
            int dbVersion = prefs.getInt(SP_KEY_DB_VER, 1);
            if (DATABASE_VERSION != dbVersion) {
                File dbFile = mContext.getDatabasePath(DATABASE_NAME);
                if (!dbFile.delete()) {
                    Log.w(TAG, "Unable to update database");
                }
            }
        }
        if (!databaseExists()) {
            createDatabase();
        }
    }

    /**
     * Returns true if database file exists, false otherwise.
     * @return
     */
    private boolean databaseExists() {
        File dbFile = mContext.getDatabasePath(DATABASE_NAME);
        return dbFile.exists();
    }

    /**
     * Creates database by copying it from assets directory.
     */
    private void createDatabase() {
        String parentPath = mContext.getDatabasePath(DATABASE_NAME).getParent();
        String path = mContext.getDatabasePath(DATABASE_NAME).getPath();

        File file = new File(parentPath);
        if (!file.exists()) {
            if (!file.mkdir()) {
                Log.w(TAG, "Unable to create database directory");
                return;
            }
        }

        InputStream is = null;
        OutputStream os = null;
        try {
            is = mContext.getAssets().open(DATABASE_NAME);
            os = new FileOutputStream(path);

            byte[] buffer = new byte[1024];
            int length;
            while ((length = is.read(buffer)) > 0) {
                os.write(buffer, 0, length);
            }
            os.flush();
            SharedPreferences prefs = PreferenceManager
                    .getDefaultSharedPreferences(mContext);
            SharedPreferences.Editor editor = prefs.edit();
            editor.putInt(SP_KEY_DB_VER, DATABASE_VERSION);
            editor.commit();
        } catch (IOException e) {
            e.printStackTrace();
        } finally {
            if (is != null) {
                try {
                    is.close();
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            if (os != null) {
                try {
                    os.close();
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }
    }

    @Override
    public void onCreate(SQLiteDatabase db) {
    }

    @Override
    public void onUpgrade(SQLiteDatabase db, int oldVersion,
            int newVersion) {
    }
}