Most companies use a dropping resistor in series with the high beam lamp for a DRL. I always hated that because it causes the high beam to burn out faster.
In any case, having the low beam on all the time during the day does make it easier for other drivers to see you. If the weather is foul, your auto lighting should turn your marker lights on as well. Or being a responsible driver, you should be.
As far as power consumption, it's such a minor drain to your alternator that fuel consumption wouldn't change.