A mistake like this will NOT make a mobius! It has a full twist, not a half twist, and does not meet the terms of the mathematical description. You can knit something like this, and it might be wearable and even fun, but it will not be a mobius.
Instructions always say to check when joining and make sure it's not twisted. But you can do that and it can still get twisted while you're knitting the first row. Making sure it's not twisted is good on the first row, but it's essential to check it before starting the second row. At that point, there's only one strand of yarn connecting at the join, and if it's twisted, it can easily be fixed.
Hope this helps.