There is no guarantee of anything, but it is not likely that you would be extradited for this type of case. However, a warrant will be issued if you fail to appear in court and you will have to return to New York in order to resolve it.
If you don't show up for your case, the Court in Montgomery county will issue a warrant. You can re-post your question in the Georgia section to see if they will pick you up and send you back based on a NY warrant.
You likely will not be extradited, however there will be a warrant issued, and if you’re stopped by police in any other state you could be arrested and held. If you don’t resolve the DWI, it is going to follow you around and create more problems than it’s worth. I recommend handling it sooner rather than later.
