Does an electric force exist between the dipoles; that is, can two objects with zero net charge exert electric forces on each other?

Answer: YES

Explanation:When two dipoles with zero net charge are brought close to each other, they will attract each other signalling that there is Electric charges can be felt by both dipoles.

Dipoles at polarized with irregular Distribution of positive and negative charges within each dipoles, once they are brought close the charge dominant in a given dipole can cause the other to attract which has an opposite dorminant charge within its dipole.