In a Honda Accord does the sports mode gear still shift up automatically?

I own a Honda Accord 2013. I've done some research and have figured out that the sports mode increases your acceleration. I've been messing with it, and the RPM's get up to 6000, and almost into the red. I don't want to blow out my engine or anything. I was just wondering does it still shift automatically, and is it safe to max out in sports mode for a decent amount of time.

Yes, but be warned. A well-ridden 10 speed bicycle will still probably out accelerate you.