Most likely. Redshift Quick-Release Aerobars are generally compatible with carbon fiber handlebars, as long as there is at least 22mm (7/8 inch) of straight, cylindrical handlebar on either side of the stem to clamp properly.
However, there are some manufacturers of lightweight equipment that specifically prohibit the use of clip on aerobars (of any type, not just Redshift's). We recommend that you check with your handlebar manufacturer to make sure that your handlebar is compatible.
As always, with carbon components, it is critical to use a torque wrench while installing the handlebar clamps. Improper clamping torque can crush or otherwise damage your handlebar, which could result in serious injury.