"What is the electrical efficiency of such a system?"
About 83% - that's the power into the transmitter unit vs. power out of the receiver. Your AC to DC conversion to supply the transmitter and the battery current to battery charge conversion are separate. To put it in perspective: your average phone charging at 2A consumes 10 watts from a 5V USB supply. If we are using a USB cable with 28AWG/0.32mm wires, the resistance of a 1m long cable is 0.212 ohms for a loss of 1.7W (two 1m long runs - supply and return). In comparison, the wireless charger has a system loss of 2.0W if adjusted to give 10W output.
A datasheet for a typical system is here:
There are some pretty clever ways they can detect foreign objects on the transmitter antenna.