How do electric anti-icing systems work?
How do they work? 

An electric current is passed through a heating element built into the device needed to be heated. For example, 115 VAC may be applied to a heating element of anywhere between 5-300 ohms (resistance values vary widely depending on the heating application). The voltage applied may be dependent on a controller that will dictate how much voltage is applied.

Using basic Ohm's Law, we can deduce that the current draw of 115 VAC across an example 60 ohms coil, would be approximately 1.9 A, and the power 220W. Keep in mind, this isn't a strict calculation as phase angle and other variables might be involved in an AC circuit - but close enough... That 220W is dissipated as heat which thus heats the device.

This is virtually the same in most GA and commercial applications. 

Are they viable? 

If by viable you mean "They work, but do have occasional failures that falls within a reasonable rate of expectation," then yes, they are viable.