Controlling multiple RGB leds with PWM from a Atmega328P using one transistor per color
Yes, this will work, but don't forget to use different resistors for different colors, because each color has different voltage.

But my opinion is to connect LEDs serially and use higher voltage (but you need to use other LEDs with NO common wire) then you get much better efficiency like example:







simulate this circuit &ndash; Schematic created using CircuitLab