wouldnt it require the Arduino to constantly looping R-G-B
Yes
making it incapable to executing other programs?
No there is time left to do other things.
What about output each channel of the TLC5940 to a LED pin
The only down side is, as you said, it takes more chips.
wouldn't it mess with the PMW pulse or creates flickers
You have to interleave the TLC load stuff so that it doesn't mess with it.
not using the LEDs' brightness potential?
Yes that is true ans it is only on one third of the time it will only be producing one third the brightness (as the eye is logarithmic it won't look a third as bright) You can compensate for this by putting more current through the LED than it could normally stand on a continuous basis.
You are talking about 3 to 1 multiplexing, I have done 4 to 1 in this project:-
http://www.thebox.myzen.co.uk/Hardware/Mini_Monome.html