Yes, of course you can do it!
It is very simple, and as you said, yes there are green LEDs at the end, but there are white LEDs too. The secret here is keeping a reasonable distance betweeen the LED and the plastic. Its function is to spread the light more smoothly than the LED does by itself, and to generate this effect.
You might have to do some tests with a plastic piece (maybe some shampoo or HDPE bottle) and try different distance between LEDs and between the piece. Try turning each LED on individually and see if you can perceive an abrupt change. You will, but at any point, and taking into account the short time between each LED, it will be as smooth as disney's one.
If there is something true about lighting and sound is that it's not only mathematics... you have to see or listen to things and make tests before doing anything, because it's all about how humans feel light/sound.
Hope being useful, and just ask if you come up with any doubt.