That separate cord for the LED's in the CPU does not affect the motor. So it shuold not affect the fan operation.
Now, the mobo CPU_LED header is for convenience, and ensures that the lights on your CPU cooler are controlled by a dedicated system in BIOS Setup. IF you have a separate header on your mobo for 4-pin plain RGB lights, or for 3-pin ADDR RGB lights, and IF the lighting system in the CPU cooler matches that other mobo header, you may be able to power and control it that way. Tell us exactly what mobo you have, and what CPU cooler you have, and we can advise on whether this really can be done.