Actually it's far from that good and may even be the reverse. What do you think those cooling towers are for at power plants. Half the energy gets 'thrown away'.
Typical electricity generation averages around 30-33% from power plant energy input to wall socket. Losses in battery charging may lose another 10-20% of it too. It's not like refilling a pail of water, it's like refilling a leaky pail of water. so you could easily be in 25% efficiency territory (not dissinilar to a modern petrol engine) and worse as you factor in electrical losses in the vehicle itself.
In comparison, modern diesel engine efficiency targets for new technology engines such as ones that eliminate the traditional camshaft are in the 40% range and large marine diesels already exceed 50% thermal efficiency.
Apparently MAN make one with ~ 57% efficiency.
Graham