cheaper???

Nope, if the pipeline was built, the instate price of natural gas from the pipeline would be based on the competitive cost of trucking LNG to the location.  This would be no different than what we pay for locally produced gasoline from Nikiski where the price we pay is based on what it costs to barge gasoline to Alaska from a West coast refiner. 

What would make you believe that having the State of Alaska go in debt building a pipeline will yield a net savings for natural gas?  If a N.G. pipeline from the N.S. were built, you will find out that the Cook Inlet gas producers will raise their prices to match the cost of the gas coming from the new pipeline.