.223 Rem/5.56 NATO needs velocity, but how much easier will it be to handle with 4" and a bit of weight snipped off the front? I use to drag around the "Right Arm of the Free World", and I never found it to be a great burden. Granted lugging a support weapon for a few exercises makes a C2 feel like a feather, so you might say I'm skeptical of the utility of a super light rifle other than having to move really fast, or shoot offhand. Unless you're kicking doors, or action shooting 24" is better than 20". One other thing to consider is that 75 ELD M's probably won't stabilize well in a shorter barrel, or not at all depending on your twist. I don't have the data to say one way or the other, but it's something to look at before you pull out the saw.
In the end is making it a little shorter really going to make a huge difference on how it handles? I haven't done the math, but cutting the barrel will have a real world effect. On one hand you can say it FEELS better with a 20" barrel, but for every inch you remove you'll reduce your effective range. .223 has two things going for it, and since we're not likely packing 300-400 rounds at a time, only one, speed.