Probably, though Soviet strategic bomber formations probably wouldn't be operating at particularly low altitude and, IIRC, the idea was to intercept before they were over target (but not far enough away that it wouldn't be problematic!) anyway, and, finally, localized EMP and flash from a kiloton-range airburst is better for people on the ground than the effects of a megaton-range ground burst.
If the Nike missiles around SF had ever been fired in anger, it would have been an effort to turn what would otherwise be total disaster into merely major disaster.
(May well have been a bored volunteer making things up, but I wouldn't dismiss it out of hand...)
My worry is what happens to critical infrastructure. For instance, if the blast were in line-of-sight of multiple high-voltage transmission lines then extra-high-voltage transformers (think >200 kV) could “melt-down” (that is to say, the cellulose insulation is damaged by higher than normal temperature of the oil caused by the excess DC current, but maybe I am wrong?). These are multi-million dollars, weigh 500 000 lbs, are very difficult to move, and have a lead time measured in years. (There are probably 10 of these on hand as spares across the country for the 4,000 currently in use.) Cascading power failure, say substantial failure in San Francisco, could affect the entire Western Interconnection. If the power goes down, so does water pressure which depends on electrical pumps. A loss of power/water for more than a week could be an extremely severe event. A military strategist wouldn't settle for just one city to be in this state either.
So if you have an attack on multiple fronts, then today it would be suicidal to potentially knock out the power to your own cities. But, maybe back when the Nike was in use power failure wouldn't be as catastrophic as it would be today OR this wasn't a possible failure mode.
Also, I argue that your line-of-sight is increased by "low-altitude" EMP blasts (30 000 ft for a localized EMP on a bomber vs >100 000 ft for high-altitude EMP) whereas a nuclear detonation probably occurs at much lower altitude (~2 000 ft), so the higher altitude could in theory attack a much larger area as far as power is concerned. So in terms of electrical infrastructure, a larger area of damage could occur by Nike attacks on bombers higher up. But who knows.