Yes, it is possible.
Ultimately, while American attempts to shoot-down a North Korean missile are unlikely to trigger an accidental nuclear war, it might not be good idea stress the Russian early warning system. The best option—time permitting—would be to forewarn Moscow of any attempt to shoot down a North Korean missile. However, during such events, there is no time to spare.
If the United States decides to attempt to shoot down future North Korean intercontinental ballistic missile (ICBM) tests using the Ground-Based Midcourse Defense (GMD) system, it is likely that Russia’s early warning system will not mistake the interceptors for a potential nuclear attack.
That does not address the question of if the United States genuinely has the capability to intercept a North Korean ICBM—and many critics doubt that it does. However, the chances are that such an attempt to shoot down a North Korean ICBM would likely not trigger an accidental nuclear war even if the possibility does exist at some level.
“There is no reason to believe that threat identification could be a problem,” Pavel Podvig, an independent analyst based in Geneva who runs the Russian Nuclear Forces research project told The National Interest.
“It is true that an unexpected event, such as a GMD launch from Alaska, would probably generate an alarm, but the system is designed to deal with these kinds of events. Of course, it would be better if it doesn’t have to deal with them, but it is not an issue of the capability of the system – I would equally not trust the U.S. system to perform adequately under stress.”