Without delving too deeply into the actual science, an electromagnetic pulse (EMP) attack would essentially fry electric circuits and knock out electricity in the affected area. Depending on how wide and for how long an area loses electricity, the effects of an EMP attack could be devastating. So much of the world relies upon electricity. Communications, banking, and transportation would be severely impacted.
The Bible does not specifically predict an EMP attack in the end times. Questions concerning an EMP attack in the end times are similar to questions concerning a nuclear attack in the end times. Does biblical end times prophecy allow for it? Yes. Does biblical end times prophecy explicitly predict it? No. The Bible predicts war in the end times, and another world war is definitely possible. However, the Bible does not predict any specific modern weapons that will be used in the end times conflicts.
The idea of an EMP attack is interesting, though. If EMP attacks were launched worldwide, rendering all technology useless, the world would essentially revert to a state comparable to that of 2,000 years ago. This would mean that the biblical references to swords, horses, etc., in the end times wars could be understood literally (Isaiah 2:4; Ezekiel 38:15; Revelation 14:20). But this is speculation. Most interpreters of Bible prophecy believe the Word of God is simply describing the end times wars figuratively, using terminology familiar to the people who lived at the time the prophecies were written.
So, could an EMP attack be a part of the end times? Definitely. Does the Bible explicitly predict that an electromagnetic pulse will return the world to the Dark Ages during the end times? No.