Yes, it can. This principle is used in some theories of dc-to-dc converters, it seems this might not work well, because the transformer output follows the input current derivative – meaning that pulsed dc input may be expected to produce exceptional spikey output.
in practice, the natural impedance of the transformer will have a filtering effect on the actual current flowing through the input, making it more than a sinusoidal signal. additional filtering on the input and output will further improve you can somehow actually induce true pulsed current on the input side of the transformer (not just the pulsed voltage) you would expect to see a very spikey voltage, not very useful output on the output side.
The pulsed dc voltage, if pulse with 0-1 changes, does not create a change in the direction of the current. the transformer is made of an inductor (connected by a metal core).
A voltage is made at the head of the inductor only if the varying flux time is applied to the dc current, this flux rises from 0 to a certain amount, inducing a change in voltage in the inductor which has no previously applied voltage. but if the flux source can not change its direction anymore, there will be no further change in the amount of induced voltage in the inductor over time.
Here we need AC current to create negative flux direction for us, thus creating constant change in voltage applied to the head of the inductor and therefore creating a time current which varies as pulsed dc currents, if the pulse goes towards negative amplitude can almost play the role ac current. the result is almost the same. (but only works for small currents and voltages)
Can be used for pulsed, in power electronics you can find a special class of transformer known as a pulse transformer or say flyback transformer. they call it a transformer but i prefer to call it coupled you should not use a normal transformer to pulsize because the dc pulsation turns more suddenly a very high induced voltage which in itself destroys the transformer.