If you get an appeal, does the case permanently stay on your record?:
The appeal must be won.  The court holds the conviction addullted, void, overturned as if it no longer exists.  Expungement of the records is another matter and that requires more legal work.  Even if that were to be granted, there is always a paper trail and just, for example, the fact that someone was arrested in the first place will always be part of that trail.  It is practically impossible to get rid of all of the record, even with a court order.