The lighter wheel will always help you going up a climb, especially when making the swap from a 404 to a 202. It's kind of like baseball, when the batter, in the on-deck circle, puts the metal "doughnut" on his bat to make it heavier. He does it to give his body the temporary feeling of weight, so when he actually does go up to bat, the bat feels lighter, and he can swing it around faster.
That being said, I don't doubt you'll come to an equilibrium, and eventually fall back to your 404 speed days, unless you reserve the 202's only for special rides.
Only when the climb is sustained and you have a low apparent ground velocity.
I bet on a course with sustained power output and longer than a few minutes the 404s would win. People tend to like rims that have a very light weight, such as the 202, because they feel snappier even if the effect is exaggerated and mental. We have tons of short, punchy climbs where I live and I've done constant power tests with 202s, 404s, and 808s and when the duration was longer than 1min and apparent ground velocity higher than 16mph, the deeper wheels were always slightly faster. I don't know about you, but even the races that have 10% gradients in them around here still climb the short steep hills really fast.
Flo wheels has some great modeling of aero vs light wheels, I'd check that out.
Also, if you actually do the moment of inertia calculations, the difference between those wheels is fairly minimal. It comes down to more than just rim weight.
Don't take me too seriously. GramzStrava