It would depend on the location of the EMP and how strong it is and how shielded it was.
Some of the EMP thing is hype. The field strength will vary by location, and the impact on electronics will vary with what the circuit is and how it is designed. I expect most of the products I design will fare pretty well, if they have been installed correctly anyway.
In the many threads on here complaining about EPA tests and standards for engine and stove exhaust emissions, I have often said that these are really pretty typical for various industries. This is a good example of that - the products I help design will have a much easier time with EMP, as they are part of the power grid and must meet US and international standards. The US and other nations have different standards, and they are quite difficult to meet. These standards are a mixture of various government and industry requirements. Prior to such standards, and presently in consumer markets where the requirements are much easier, the equipment would be much less capable of surviving a high energy transient.
Learning how to do it well took many years, and it is often a a real PITA - the standards keep changing, they are often poorly written and subject to different interpretations. But now that we have that knowledge/capability it is a huge advantage for us in the market. I see things designed by people who failed to learn the rules first and haven't got a prayer of passing - that is what would be offered to the market without the standards forcing the development of ways to pass them.