And sometimes move for an appellate court order staying the order of the trial court, if the trial court's order would have an irreversible bad effect.

It seems to me that the person to appeal would be the holder of the Gmail account. If no one hears from him, which is likely (The Gmail account is probably abandoned), then nothing will happen.

I just hope that this doesn't set a precedent in future cases.

Has Google complied with the order yet?

I would hope that Google would see it in their interests to appeal. Considering the judge's history, odds are an appeal would go through pretty well and Google gets to keep its reputation in tact for a relatively low cost.

There are other methods to help out the bank without setting this precedent.