Will a lightning strike to a tree near by cause an EMP that will cause a surge on all wires in the house?

There are coconut trees all around our house (tall ones). They are likely to be hit by lightning strike... will the Electromagnetic pulse generated by the strike cause the wires inside the house to have a surge? I have installed a surge protector but wouldn't it be pointless if the EMP introduced the surge to wires after the protector? Also does the EMP raise the voltage on DC circuits? if so wouldn't that mean cell phones will be damaged as well?