True, there will be an energy cost from imperfect efficiency. The EROEI (energy returned on energy invested) will necessarily be less than 1. But if the hydrogen produced is cheaper than hydrogen produced by natural-gas reforming, then it's still a gain.
To get an idea, I'll use current fossil-fuel prices and electricity-generation efficiencies.
I'll use these recent US numbers:
Coal Prices and Coal Price Charts - InvestmentMinePetroleum -- 60.49 USD/bbl
Natural Gas -- 2.93 USD/mmBTU
Thermal Coal CAPP -- 51.25 USD/st
CAPP = Central Appalachian
How much coal, natural gas, or petroleum is used to generate a kilowatthour of electricity? - FAQ - U.S. Energy Information Administration (EIA)1,842 kWh per ton of Coal
127 kWh per Mcf (1,000 cubic feet) of Natural gas
533 kWh per barrel of Petroleum
Assumptions:
Power plant heat rate -> energy efficiency
Coal = 10,498 Btu/kWh -- 33%
Natural gas = 8,039 Btu/kWh -- 42%
Petroleum = 10,991 Btu/kWh -- 31%
Fuel heat contents
Coal = 19,336,000 Btu per short ton (2,000 lbs) Note: heat contents of coal vary widely by types of coal.
Natural gas = 1,023,000 Btu per 1,000 Cubic Feet (Mcf)
Petroleum = 5,861,814 Btu per Barrel (42 gallons) Note: Heat contents vary by type of petroleum product.
So I find:
Oil: 0.113
NatGas: 0.024
Coal: 0.028
all USD/kWh
That makes crude oil about 4.3 times more expensive for generating electricity than natgas or coal. That also makes the raw energy content of oil cost 0.035 USD/kWh, about 1.35 the cost of electrical energy generated by natgas or coal.
Using a natgas-coal average, 0.026 USD/kWh, if production of some synfuel is only 50% efficient in applied electrical energy, then that synfuel's energy content will cost 0.052 USD/kWh. But if the price of oil goes up by a factor of 2, then its raw energy content will cost 0.070 USD/kWh, and the synfuel will undersell oil.
Also, since wind and solar electricity generation are still-growing technologies, their price per unit electricity may drop further. If they drop by a factor of 2, then that will cancel out my assumed 50% synfuel efficiency factor.