No — that's a myth. The myth may have arisen from the fact that cold water does absorb heat faster than hot water. However, once the water gets to a hotter (not yet boiling) temperature, it absorbs heat at a slower rate, and from that point it takes just as long to bring the water to a boil as it would if the water were hot to begin with. And because it takes cold water some time to reach the temperature of hot water, cold water actually takes longer to boil than hot water does.
It makes sense: The hotter the water, the closer it is to boiling, therefore, the hotter the water, the faster it boils!