It seems like an obvious answer - yes - but have you ever thought about the math behind it? Obviously it takes less energy to accelerate a car from a rolling start to a given speed than it does to get it to the same speed from a total standstill. Bear with me through some sketchy math here. I'm going to make some pretty gross assumptions - a good median weight for a family car is 1500kg nowadays, and a good acceleration figure is 0-50km/h in 4 seconds. What follows assumes no complications from friction, wind, losses through transmission and the myriad other things that affect overall energy figures for a car, but this at least will serve to give some idea what I'm talking about.
Assume we have a stop sign and we have two options - come to a complete stop, then accelerate away at a constant rate to reach 50km/h, or cruise through at 15km/h and accelerate back up to 50km/h.
For the first scenario, the acceleration rate is 3.47m/s² (v=u+at), and assuming you reach 50km/h, you'll travel 27.7m (s=ut+½at²)
Assuming constant acceleration (which makes this much simpler), the force required in this scenario is 5205N (F=ma) which means that the energy expended is 144,178 Joules (W=Fs)
Okay yes that's a very simplified explanation, but it does give us a tangible number.
For the second scenario, assume we're going to travel the same 27.7m after the stop sign but this time we're going to coast through starting at 15km/h instead.
Now, the acceleration rate is less - 2.43m/s², meaning the constant force is also less at 3645N. With less constant force over the same distance, the energy expended also drops, in this case to 100,966 Joules, which is 30% less.
I'm not going to go into the math of fuel consumption vs. vehicle weight vs. acceleration but it's safe to say that for 30% less energy, you'll probably burn 30% less fuel.
Add up the number of red traffic lights and stop signs that you come across during your daily commute, and think how much better your overall fuel economy would be if you burned 30% less fuel at each of those stops. Over a day, a week, a month - it would add-up.
Maybe the time has come for the U.S to adopt roundabouts and get rid of stop signs completely. Roundabouts are more efficient all around - you don't often come to a complete stop and they flow the traffic much more smoothly. I'm sure someone could write a properly-worded paper and put it in front of the politicians and short of being lobbied by Big Oil, there's really no good reason to have stop signs any more.