Could You Use Common cathode RGB LED without providing power to G and B
Of course.

Your RGB LED package electrically looks like this:



It contains three LEDs that have their cathodes wired together, so presents a total of 4 pins.  Not running current thru any LED isn't going to affect the others.

Note that the point of a RGB LED package is usually to allow arbitrary colors to be displayed.  If you had to run all the LEDs at the same current, you wouldn't really have any overall color choice.