Is it possible to be electrocuted from a properly functioning GFCI circuit?
Yes you can be electrocuted even with an operating GFCI. A GFCI will only trip if current goes from the hot and does not return on the neutral. That means it will trip if you stick a fork into the hot and jump into the bathtub / touch the fridge while holding it (because the current on the hot is NOT seen on the neutral - the power is escaping through the water or fridge chassis to ground).

A GFCI will not trip if you grab one fork in each hand and respectively stick one fork into the hot and another into the neutral (because all the current on the hot is also seen on the neutral). At that point, you're relying on the current operated circuit breaker, which will only trip once the current exceeds its rating (which it may or may not do while going through your relatively high-resistance body).

GFCI's limit shock to a low level, fail often, and are a good supplement (defense in depth). http://www.thecircuitdetective.com/gfis.htm