he is a proposed solution which i found in stackoverflow
File dbfile = new File("/sdcard/android/com.myapp/databases/mydatabase.db" );
SQLiteDatabase db = SQLiteDatabase.openOrCreateDatabase(dbfile, null);
System.out.println("Its open? " + db.isOpen());
here is the link.
UPDATE
i am not sure you can use this along with SQLiteOpenHelper, but you sure can query the database object.
db.getVersion();
db.execSQL(sql);
db.beginTransaction();
db.endTransaction();
db.setTransactionSuccessful();
db.query(table, columns, selection, selectionArgs, groupBy, having, orderBy);
you can do all the things which you expect with a database. SQLiteOpenHelper in only a wrapper class which helps you the extra which we always can do on our own.
EDIT
as for your file size limit i found this link. Is there a file size limit on Android Honeycomb?