Indeed so.A storage heater uses entirely resistive heating elements, at least every one I've seen. Ohm's law will hold with a simple resistive load, and the current will drop as the voltage reduces.How about, for example, a storage heater? I was told that a FCU was not suitable for one with 3x 850w elements, as if the voltage dropped, the current would increase and blow the fuse (potentially). (Sorry I am going a little off topic here.)
Of course, if the resistive load is, say, thermostatically controlled, then the lower voltage (hence lower current) will result in the current flowing for a greater proportion of the time - potentially (if the control is perfect and the capacity of the heater adequate) to the extent of consuming the same amount (e.g. kWh) of electricity as would been the case with a higher voltage and current (but 'switched on' for less of the time).
Kind Regards, John