You will need to find out from the New York State Department of Motor Vehicles if you will have any difficulties applying for and receiving a driver's license with your foreign license being suspended.
Normally with a valid foreign driver's license the NYS, and other states, allow you to drive without obtaining a US license for a certain period of time however since your foreign license is not valid you would be unable to use this license to drive while in the States.
Since you do not have a valid license to turn in you will have to see what steps the NYS DMV requires you to take in order to acquire a driver's license and legally drive in the United States.
The information that the NYS DMV gives for those that are turning in a foreign license for a New York license include:
To obtain a license in NYS you must pass a written test, complete a 5-hour pre-licensing course and pass a road test.
You must show a social security car or if you are not eligible for a Social Security Card, you must provide a letter or form SSA-L676 from the US Social Security Administration (SSA) that states that you are not eligible. The SSA Letter or form must have been issued no more than 30 days before the date of your application.
When you receive your NYS driver license, you must surrender your foreign driver license to the DMV road test examiner. The local DMV office keeps your foreign driver license, and then destroys the license after 60 days.
To see if these steps apply to you even without a valid foreign license to turn in or if your suspension in your home country will affect your ability to receive a license in New York State contact the NYS DMV directly. The number to call from out of New York to speak with the DMV customer service is 518-473-5595.