The wiki page on EMP is an interesting read.
Yes, but so unspecific as to be vague about what might/could/may happen(!).
Chances are it could possibly damage the computer system(s) that control local power and telephone grids, and their transfer/backup switching systems. The common [flat] cellphones can be damaged enough to not receive signals afterward, and possibly (less than 50% chance) of the 'flip-phone' cell phones' receivers being damaged. Power transmission gear would not be hurt, at least not very much, but the rush (since 2009 or so) to put it all under cheap Chinese computer's control (i.e., Chinese-built PLCs and HMI systems) has made the grid itself vulnerable to a 24-48 hour shutdown from one EMP event over a major city, for example. The powerplants are often near those cities, and they, too, are run with Chinese-built PLCs and HMI gear.
So, buy a nice little Honda generator (2kW or more) and review your house's electrical box to learn where you can disconnect the main breaker and jumper in your own power, then you won't be so vulnerable, and can keep your 'fridge (and gas furnace, if winter) running. I have an RV that can also be employed for the same purpose (including bugging out if the neighborhood becomes a problem?), including taking a shower.
While an EMP attack (supposedly a sequential one over several days) is the 'gamed' scanario for attacking the USA, it would literally take thousands of them, over a 10-20 day period, to shut things down for more than a few days per event in each area attacked. Such is the advantage of NOT having the government making your power, gas, fuels and groceries.
