Not significantly. RGB lighting that operates by itself does not affect the CPU at all. Some lights are changed with a button control or the like rather than by a program that runs on the computer; those have zero overhead.
Some RGB lighting has a driver that controls it; that driver runs once in a while, and whatever CPU time and memory it uses is not available for other uses. But it’s minimal, and unless your computer is on the ragged edge between working for your tasks and not working, you won’t notice the overhead.