Yes,
Current is the flow of electrons. At zero resistance the flow of current is similar to motion at 0 gravity or in outer space where there is no drag to stop the motion. These types conductors are called superconductors.
In a superconductor, the current can keep flowing forever since there is no resistance. But since conductors have inductance (in fact, superconductors are used most often to create magnets like for an MRI scanner), applying a voltage would not (immediately) cause an infinite current to flow.