They already have LNG port. The largest cost in Natural Gas transport is the liquification and the vaporization operation. There would be no justification build that pipeline and still convert to/from LNG.
The pipeline is only economic if it avoids going to LNG altogether and stays gas pipeline to pipeline.
Avoiding ship travel around the Saudi Peninsula while still going to LNG does not justify the pipeline.
I think you are missing a larger point. The conflict in the Middle East has evolved into a widening Shiite/Sunni rift. A pipeline from Iran to Syria via Iraq would represent a pipeline beyond the control of Sunni energy powers, and to the Shia that matter more than raw economics. Assad is a Shia Alawite and that minority rules Syria.