Combining Arduino and LEDs on same power channel
It's a good idea in general to keep the power for your logic and power devices separated. Motors for instance will generate a lot of noise on your power, and to some extent this may pass straight through the voltage regulator, polluting the microcontroller's \$V_{DD}\$.  

One way to keep power supplies separated is feed them via a diode from the common power source. Place a buffer capacitor after the diode, sized for the expected load.

If the LEDs are controlled statically this should be less of a problem than for motors.