You have described 1950 era ABM's, so the short answer is "Yes, of course"

The pulse of hard radiation from the nuclear explosion could potentially fry the electronics of the incoming warhead, so the detonator does not work. The sheet of neutrons from the explosion could actually affect the nuclear material inside the incoming warhead, and of course the thermal pulse will abate part of the incoming warhead and act like a rocket motor throwing it off course. If the explosion is close enough, the enemy warhead is simply consumed inside the fireball.

The US "Sprint" ABM deployed briefly in the 1970's, and was armed with an enhanced radiation thermonuclear warhead. Older systems like Nike or air to air missiles like Genie also used nuclear warheads (although the primary purpose was to destroy the bombers carrying the nuclear warheads, the effects of the explosion on the Russian bombs outside the immediate blast radius would be quite similar).

The downside is you are using nuclear weapons in the atmosphere in the airspace over or near your own homeland, and the enemy warheads are either disintegrating in the atmosphere (showering you with Plutonium dust), or are plunging randomly into the ground, leaving you with the task of recovering "hot" items full of nuclear warhead fuel. While much preferable than dealing with the aftereffects of a nuclear explosion vaporizing a city, it is still not an ideal solution, hence President Ronald Reagan's Strategic Defense Initiative; meant to shoot down ICBM's in the boost and mid flight stages rather than stopping warheads in the final seconds before impact.

You have described 1950 era ABM's, so the short answer is "Yes, of course"

The pulse of hard radiation from the nuclear explosion could potentially fry the electronics of the incoming warhead, so the detonator does not work. The sheet of neutrons from the explosion could actually affect the nuclear material inside the incoming warhead, and of course the thermal pulse will ablate part of the incoming warhead and act like a rocket motor throwing it off course. If the explosion is close enough, the enemy warhead is simply consumed inside the fireball.

The US "Sprint" ABM deployed briefly in the 1970's, and was armed with an enhanced radiation thermonuclear warhead. Older systems like Nike or air to air missiles like Genie also used nuclear warheads (although the primary purpose was to destroy the bombers carrying the nuclear warheads, the effects of the explosion on the Russian bombs outside the immediate blast radius would be quite similar).

The downside is you are using nuclear weapons in the atmosphere in the airspace over or near your own homeland, and the enemy warheads are either disintegrating in the atmosphere (showering you with Plutonium dust), or are plunging randomly into the ground, leaving you with the task of recovering "hot" items full of nuclear warhead fuel. While much preferable than dealing with the aftereffects of a nuclear explosion vaporizing a city, it is still not an ideal solution, hence President Ronald Reagan's Strategic Defense Initiative; meant to shoot down ICBM's in the boost and mid flight stages rather than stopping warheads in the final seconds before impact.