If you fail to appear in court, or otherwise legally take care of the speeding ticket you received in Virginia, you may be convicted in absence, issued a higher fine, and possibly have your license suspended. There will also be a trial in absence fee. The VA DMV states that failure to pay will result in license suspension. Thus until you take care of the speeding citation you cannot legally drive there if your license is suspended by the State of Virginia.
Virginia and New York are both members of the Drivers License Compact (DLC) and Non-Resident Violator Compact (NRVC). As members of the DLC it means that if you were convicted of the speeding offense in Virginia that the VA courts would then inform the New York Department of Motor Vehicles of this conviction.
The NYS DMV does not record convictions of moving traffic violations by NYS non-commercial licensed drivers in other jurisdictions, except traffic offenses committed in the provinces of Ontario and Quebec, in Canada. Therefore, except for traffic convictions in Ontario and Quebec, out-of-state traffic convictions are not added to your New York State "violation point" driving record.
The NRVC requires member states to suspend the license of a driver who gets a traffic ticket for a moving violation, such as your 15 mph over speeding ticket, in another state but fails to pay or otherwise legally comply with the citation.
The NYS DMV discusses this by stating that your New York State license will be suspended if you fail to answer a ticket for a moving violation in any state except Alaska, California, Michigan, Montana, Oregon or Wisconsin (states that are not members of the NRVC).
Furthermore, your license will remain suspended until you answer the ticket. Likewise, drivers from any state, except those from the six states listed above, will have their driver licenses suspended in their own state for failure to answer a moving violation summons in New York State.
So if you decide to not pay the Virginia speeding ticket then likely your license will be suspended in both states until the issue is taken care of in VA by either paying the fine or complying in some other manner with the citation.