Yes, but it is a limited right on several fronts. First, the creep was convicted, and the appeal would have to come from the losing side. I don't think the pervert is going to appeal it.
Second, the sentence can be appealed if it is believed to be an illegal sentence. I have no idea about Vermont's sentencing structure. I know that Tennessee is a sentencing range state, meaning that each conviction has a set minimum and set maximum for the range of conviction of the particular offender. For example, someone in Range I (zero or one prior felony conviction) would get a sentence between one and two years for a Class E (least serious) felony, and would be eligible for release after completing 30% of that time. So if a judge sentenced a Range I offender to three years on a Class E felony that is an illegal sentence and is reversible on appeal.
Third, as with any appeal, there must be demonstrated that a significant error of law was present in the original sentence. Technically, almost every trial has errors. For a sentence to be overturned on appeal the error must be significant in the eyes of the appellate court. Not allowing a witness to testify when they should not have been excluded is an example of significant error.
That being said, the best remedy in this case, again with no knowledge of Vermont law, would be an active campaign to have this judge sanctioned by the state bar, and a campaign of public outrage to make sure he never spends another day on the bench. His actions are absurd, unethical, and improper. He has done a monumental disservice to the people of his judicial district, not to mention to the victim in this case. I can only imagine the capillaries that blew in the District Attorney's brain when word of this injustice reached him/her.