Safe to use series resistors for powering common anode RGB LED from single constant current source?
A constant current source is a voltage source with a feedback loop that regulates current.   The purpose is to avoid the current limiting resistors that waste energy and/or provide more precise control of brightness without needing PWM.
You've designed a circuit that adds the PWM and current limiting resistors back in, in which case using the constant current source is unnecessary.  Either use a constant voltage source, or get a constant current source with a PWM input to control brightness.