No. Appeals are made after the preliminary trial and are solely questions of law and not questions of fact. This means that appeals will never question the jury's finding, but rather question a judge's decision that could have caused the jury to find differently. (I.E. A piece of evidence is presented and the jury uses that evidence to find someone guilty. The appeal will be that the judge was wrong to allow that evidence to be seen by the jury in the first place, not that the jury was wrong from coming to the conclusion it came to because of the facts presented).
In criminal trials and only criminal trials, the initiation of the appellant process is the sole right of the defendant. This means that the prosecution cannot appeal primary case's decision, but they can appeal an appellant decision. Basically its a fancier way of saying "No Double Jeopardy" but it still logically holds: If you are found guilty, the Prosecution will agree with the finding and you won't, so they wouldn't appeal anyway, and if you are found innocent, you'd be an idiot if you appealed. YOu're not going to jail, even if you thought the judge was wrong, why would you trow that verdict away. And it's unconstitutional for the state (i.e. the entity represented by the Prosecutor) to have a second primary trial based on evidence that was not presented in the first trial.
Since the Appellant process is based on the judge's incorrect decision affecting the outcome of the case, so long as the case has not been heard by the jury and has not been dismissed (i.e. the judge won't let the case get to the trial stage) the case is tossed. A trial begins when the jury is seated, and ends when the verdict is rendered or the judge dismisses and by doing so, does not allow a verdict to be rendered.
There are proper remedies for the scenario during the trial, including the defense convincing the judge to declare a mistrial (which is when the impartiality of the trial is compromised to such a degree that the jury's verdict may be affected. This isn't an appeal so much as everyone pretending that the first attempt at a trial never happened. The prosectuion may refile and a new jury is seated). This however is a judge's sole discretion, so he's not likely to make a ruling and then here that the ruling is so damaging that the trial is compromised (especially prior to trial).
The other option is jury nullification. This occurs when the jury renders a not guilty verdict not because the defendent did not do the crime, but because the "crime" should not be a crime in the first place. This is not something the defense can directly ask the jury to do but may suggest. (i.e. If the Defense hints that the jury can render the verdict in such a way that overturns the law, it can result in a mistrial at the prosecutions motion for one. However, the defense can argue that fire arm implies that fire (even a small one) is involved in the weapon to propel the projectile and that a bow and arrow can be fired without any flame (flaming arrows don't count as they're not using the fire when launched but on impact). If the jury agrees that Firearms specifically require the use of flame as a component of propelling the projectile and thus a bow and arrow is not a fire arm, their not guilty verdict will effectively set case law that bars this judge and others at his level from allowing a similar incident in that jurisdiction from being an considered an offense under the ordinance used (this can be patched by changing the law from fire arms to projectile weapons, which a Bow and Arrow is considered, even if it is not a firearm.).