No, and yes. Sure if one siphons off gas at one end that leaves the market you reduce supply and that will have some measurable effect on prices. That being said, the true price pushers in the US are bad gas infrastructure due to green activism. If there is no pipeline from the gas field to demand centers, the gas cannot go there. If gas has an LNG terminal as an outlet but has no credible way to get to the North East where prices are really high, it does nothing to alter prices in the North-East even when it leaves the Lower 48. Bad policies blow up prices, not some terminals.
Framed around projections that U.S. consumers could be hit with higher heating bills this year, advocacy groups are renewing the message that expanding