Hire a criminal defense attorney to resolve this matter before you go to court. They can explain and expedite the process.
An ACD is certainly possible. Bite the bullet, pony up a few bucks, and retain a criminal defense attorney familiar with the court where your case is returnable. Hiring a lawyer in advance will a) get you someone who can sit down with you and explain the process to you, b) allow the negotiating process with the DA's Office to begin in advance of your court date so everything is lined up and ready to go when you get to court, c) expedite things on your court date to minimize your time waiting around.
Hire a criminal lawyer. You already made a mistake by paying the civil demand because they would not have sued to collect. New York does not expunge.
I am a former federal and State prosecutor and have been doing criminal defense work for over 16 years. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012 and 2013. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. Martindale-Hubbell has given me its highest rating - AV Preeminent - in the areas of Criminal Law, Personal Injury, and Litigation. According to Martindale-Hubbell”AV Preeminent is a significant rating accomplishment - a testament to the fact that a lawyer's peers rank him or her at the highest level of professional excellence." Fewer than 8% of attorneys achieve an AV Preeminent rating. I also have the highest ranking – “superb” – on Avvo. The above answer, and any follow up comments or emails is for informational purposes only and not meant as legal advice.
If you retained a criminal lawyer he would have told you to ignore the civil demand letter. Retain a criminal lawyer to get an ACD and make better decisions in the future.