You may struggle as the forward voltage of the green and blue dies is often >3.3V. They may work at a lower voltage but add to that any possible constant current driver dropout these devices use to drive the LED's (to get consistent brightness from all three dies) and they could be substantially dimmer. With that said, I suspect they just use resistors as I've found the colour to vary significantly with varying VDD.
I would say 3.7V is the minimum these should run at. If its just for indication, rather than specific colours then 4.2 down to 3.7V should be OK, and would satisfy the VCC*0.7 requirement for the data line.
As a more expensive option, you could use a small 8 pin micro to drive an RGB LED. Less quiescent current and more control - at the cost of more complexity, code to write etc..