If your application is still active even after the fingerprints, they will probably force you to go to a Fitness Interview to question you about your convictions. They would have denied you WAYYYY before you got to take the class.
Sorry, but in New York State, it is a misdemeanor to refuse a a chemical test if the officer has suspicion to believe you are intoxicated or under the influence of narcotics.
however, because you do not have any dmv points i think they will just get you an interview with a TLC inspector. Don't be surprised if you get denied though.