When you think of a Fretlight Guitar, think of a car that has a built-in navigation system that tells you where to drive. The car still runs great whether the navigation system is turned on or not, but you will certainly get to where you want to go faster and more efficiently if you use the navigation system! (unless you have a 4x4 and know some off-road shortcuts!)
The Fretlight works much the same way. The guitar itself IS a guitar, and it has no idea that there is an amazing light system built into it. The light system similarly has no bearing over the guitar itself. These two systems do not mingle with each other at all inside the guitar. However, the light system is powered by your computer, so to light the lights you must have the computer cable plugged in. So the answer to this question is both yes and yes. You can plug into an amp with or without the guitar plugged into the computer (or back to the car analogy: with or without turning on the navigation system) and yes you can also just plug the guitar into the computer to light up the lights without it plugged into an amp.