Yes you will get red sex link chicks with that combination. I don't know exactly what the chicks will look like as far as other colors and patterns, but the males will be yellowish and the females reddish. We are talking down color, not feather color, so this works best with just hatched chicks. There is a correlation with down color and feather color, but I've had some strange colors show up as the chick feathers out. With my mutts, some chicks feather out quite a bit differently than you would expect by looking at the down.
With some crosses, the difference is real obvious. The males are clearly yellow and the females are clearly red. With some crosses, like when you use a Buff Orp male over some silver hens, the difference is not as clear as you would think. It really helps in those cases to have both males and females in the hatch so you can compare one to the other.
I don't have any experience with New Hampshires. I think they are lighter than some of the dark red birds, so you may need to have some males and females chicks to compare to each other, especially your first time, but I'd think the difference will be pretty obvious when you see them together.
One word of warning. This works best if you don't have any other red or yellow chicks from other breeds in the hatch. You might be able to tell by striping or something like that, but it is real easy to get confused which are which if you have other red or yellow chicks in the hatch, especially your first time.
