I think they do, but the reason they don't start with enough fuel to finish the race is because of the time penalty it would cost them in qualifying, so rather they will go slower later on in the race when it is likely they will have a margin over the driver behind.
What time penalty in qualifying? In Q3 they can run with as little or as much fuel as they like. They fill up with fuel between qualifying and the race, this is the second season of operating in this way.
The time penalty starts in the early part of the race. With sufficient fuel to complete the race at full speed the car would be very heavy and hence slow. Computer simulations show that fuelling a bit light, then having a fuel saving section between two full speed sections results in a faster race.