Yes, the bike stumbles badly. I'm not sure if it cuts fuel, or spark, my guess is fuel. I've hit the rev limiter many times, its not a big deal. And, its really not necessary. The bike doesn't need to be at the top of its rev range to make power.
Go out and hit the rev limiter a couple of times and find out how it feels. You'll also learn how the engine sounds way up there and find that you don't need a tach to know where the power starts to fall off.