Would it influence the judge? Maybe, but modern jurisprudence strongly disfavors anything that enables litigants to choose their own tribunal. The question of whether the American legal system does a good job of that notwithstanding, the problem is that if you enable a defendant to get another roll of the judge dice by assaulting the first assigned judge, you've created a perverse incentive to assault court personnel in a non-zero amount of cases. You don't want to allow for the possibility of rewarding a defendant for bad behavior. Consider:

Capital defendant is on trial for murder. The first judge they draw is strongly in favor of the extreme penalty. The alternative with a different judge would be life--maybe even with the possibility of parole, depending on the jurisdiction. If convicted, the sentence for assaulting a judge is always going to be less than death. Ergo, if you're the defendant in this case and have the opportunity to assault the judge, knowing that doing so gets you a new judge, then rationally you should assault the judge. Courts generally expect litigants to be rational. That is, if the penalty for x is less than the risk value of y, a reasonable litigant will do x, even if x is jumping over the bench to take a swing at the judge.

That's no good, and it's not a new phenomenon. Usually this kind of "forum selection legal game theory" applies in questions wherein a litigant has the choice to initiate an action before one of a number of courts, and forum (and judge) shopping is a major topic in legal academia. [It's not an accident that Aileen Cannon is Trump's judge of choice.]

All of that said, should this judge recuse herself? Personally I don't think so, for the aforesaid reasons, but I also don't want to give the impression that it's cut and dry. Being pragmatic, many judges wouldn't want the hassle of being personally invested in this kind of debate. Some might stand on the principle (and they would be right), but in my experience, most judges would rather take a punch in the face than be reversed on appeal.