Display current will likely be lower in mutiplexed displays, because only one display is lit at a time. For example, if you have a non-mux four-digit seven segment display with each segment drawing 10mA, displaying "8888" would be a total of 280mA (not including decimals, colons, etc.). With the multiplexed display, while the current will need to be higher per segment to get the same brightness, only one display is active at a time, therefore the total current should be lower. One problem: if your multiplex clock stops running at the higher segment current and leaves one digit "on" all the time, the excess current could damage/destroy that display.
JB