Theoretically, it would. But the distance involved through pipes that large mean a siphon cannot establish flow. Even theoretically, you’re asking it to go over two very, very large mountain ranges: The South Pass in Wyoming is 7500 feet.
Also, siphons “break suction” at the point where the surface vapor pressure of the water’s free surface exceeds the vacuum “pull pressure” on the “tube” of water in the pipe. So you cannot go “up” against gravity that far without the water vapor ending the vacuum that is providing the motive force.
OK, how about lots and lots of very little syphons...capillary action (just kidding).
Your vapor pressure argument convinces.
Of course, they could hire Swiss tunneling experts to mediate that problem... just drill some holes through those mountain ranges...nothing a few $bln wouldn’t sort out ;)