Lots of guys play through broken bones and similarly restricting ailments. It is fairly common. My junior year at Cal one of our starting OL rarely practiced during the season due to weekly draining of his knee but never missed a game. He would play 50-70 OL snaps on Saturday and come back Sunday with a knee the size of small watermelon. He ended up playing 9 years as Elway's center in Denver.
If KA's wrist was not casted and/or heavily wrapped during games, I imagine the break was to a small bone that didn't impact range of motion and strength to a great extent. Not only is it not hard to keep that hidden, but you really do NOT want opponents knowing about it. They will target it repeatedly.
That said, you are right that a broken wrist is a very tough injury for a receiver as they use the wrist for everything from catching balls to blocking (frankly, every position does). Try catching a hard thrown ball with a broken wrist, it ain't easy.
I broke my wrist in high school and missed several weeks of the season in a cast. Of course, I was not a potential first round NFL pick and my high school did not make boatloads of money from our team's performance, so my absence was not as impactful either on or off the field as KA's would've been to Cal.
