I have an alt myself that ses Air Stomp, even though I don't find it as effective, it is funny to chain in a stomp kill or two! The lack of fall damage can help a bit, but not hugely, seeing as there's only a very small number of falls in the MP that give fatal damage on full health.
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Then you do not jump off buildings very much.
I find it helps greatly....but I always get to the top of the map quickly to scout with my visor.
Also, No fall damage means you can keep running non stop. Very hard to do after getting hurt or armoring up to take the fall.
Oh, I do jump off a lot, but what I do is make sure I glance the sides as I fall to slow me, and then I usually don't take any damage. No need to armour up, and never get the slam animation. The small benefit it'd give me IMO is outclassed by the reduced pit stops Nano Recharge gives me as I literally never stop running and jumping.