Sure you can. The docs are a little conflicting about this as they also say that no limitations are imposed. I think they should say that relative paths are to the above location and dbs there ARE private. Here is the code you want:
File dbfile = new File("/sdcard/mydb.sqlite" );
SQLiteDatabase db = SQLiteDatabase.openOrCreateDatabase(dbfile, null);
System.out.println("Its open? " + db.isOpen());