Molecular solids are held together by covalent bonds in which the atoms of the bond are sharing electrons. Because they are sharing the electrons, there are no unbalanced ionic charges to conduct electric current. Consequently even when dissolved in water they will not conduct electricity.
Not all molecular solids will dissolve in water. The determining factor will be the polarity of the molecule. The more polar the molecule the more readily it will dissolve in water. However, even polar molecules do not dissociate into ions, and thus they do not conduct electricity either.