Will an out of state drivers license suspension show up on my license in my state of residence?

There is something known as the Interstate Drivers License Compact, which is an agreement between 45 states to share information regarding one's drivers license.  New York and Virginia are part of the compact and share information mainly regarding DUI convictions, but they also exchange information concerning license suspensions and traffic violations of non-residents and forward them to the state where they are licensed known as the "home state."  Its theme is One Driver, One License, One Record. The home state would treat the offense as if it had been committed at home, applying home state laws to the out-of-state offense. So yes, New York will know.