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As you are billed on the consumption of wattage and wattage is the product of amp times volts the answer to your question is yes. An increase in current will result in an increase in electrical consumption.

Additional Answer

Residential consumers are billed on their energyconsumption (there is no such thing as 'electrical consumption' as 'electricity' is not a measurable quantity!), expressed in kilowatt hours.

There may be several reasons for an increase in load current. For example, if the residential load has a low power factor, it will be drawing more current than necessary, but the energy consumed will be no different from if the load had a high power factor.

So, for residential loads, an increase in load current doesn't necessarily mean a higher energy consumption.

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Q: Does a increase in current result in increase in electrical consumption?
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