Everything is relative, so yes, it will conduct electricity--but very very little compared to city water, well water, or salt water. The reason is that the way a liquid conducts electricity is by the positively or negatively charged ions that are in it actually moving from one of the electrodes to the other, carrying charge (electricity) with them. Salt water has salt in it, NaCl, which readily ionizes or dissociates to ions of Na+ and Cl- which can float through the water carrying charge and thus conducting electricity.
Distilled water is water that was boiled to steam and recondensed to water. Virtually all the salt that was originally in it is left behind as the pure water boils away. So distilled water is
relatively pure H2O (HOH). Water can ionize to H+ and OH- like salt does, but it ionizes to a far, far, far, lesser degree and is therefore very resistant to conducting electricity.
Will distilled water conduct electricity