Would disconnecting the white cable from a Verizon FiOS Set Top Box screw up FiOS service?

I don't have FIOS, which is a fiberoptic system, but I worked in fiberoptics for many years. If the "white cable" is the fiber input cable, it's carrying a laser light that you don't want pointed at anything that could be damaged by a laser, like your body parts.

In reality, the power level of the television laser is very low, so the practical hazard is minimal. Still lasers are inherently dangerous, and we learned in the business to treat them like loaded guns. So I think you can temporarily disconnect it from the FIOS receiver without harm providing you ensure that the loose cable is secured in a manner that points it away from anything you don't want laser'd.