I can't tell you without seeing your commission plan documents and even then if it is not addressed, it is a 50/50 call. Generally the employer doesn't have to allow you to work out your notice and can terminate you immediately. You might be eligible for some unemployment benefits depending on NY state unemployment laws.
If your plan said you have to be there the full month to earn the commission, then no they wouldn't be required to pay it. Your choice is to quit right after getting a commission with no notice OR hope your employer keeps you for that time OR ask if they terminate you to allow you at least partial month's commission through that day.... If you quit with no notice, they could put that on a reference.
But if you do quit and they don't pay commission and that commission is usually used to pay the minimum wage/OT owed (assuming NOT outside sales), they would still owe you minimum wage and/or OT for all hours worked for that time period. No, probably no where near your commission amount but more than $0

