I'm not sure this would even make sense to build - the purpose of a nuclear deterrent is to ensure that a first strike against the power in question is rendered impossible under rational conditions. If both sides have been reduced to ash, there hardly seems a point to maintaining that kind of posture - it's inconceivable that a war could be fought under the conditions that a mass nuclear exchange would entail.

What would there even be left to fight for? Once the first salvos have been launched, the rest of the arsenal becomes essentially useless.