In theory yes, in a practical sense, probably not.
It would certainly not be cost effective from a fuel perspective.
To get past this, you could do as is done in Spain and put the water in tanks and simply let the Texas heat evap the water (much of the table salt in Spain comes from a facility in Cadiz which captures ocean water in open tanks and then lets Mother Nature remove the water; their location is both sunny and windy so the evap process is surprisingly quick).
I think the larger concern would be as the manager of that facility explained to me - the mixture of chemical constituents in the collected water is not at all consistent. PPM of the elements DOES vary in the water so one batch may be high on one chemical and low on another. They had to adjust the process they used to strip out all the undesirable stuff to end up with edible salt (increase / decrease the "stripper" chemicals used to remove stuff they didn't want in the salt).
I would be concerned you would find this same variation.
I think the Red Sea salt is created in kind of the same way as you suggest - but their volume probably allows them to mix tons of product in an attempt to ensure the end result makeup of the salt in the bucket is "really close" to that necessary to make "seawater". Also, they may be using the salt waste from the same evaporator they are using to make the water they need to run a steam powered ship (I ran these in the Navy, all fresh water for the people and the boat was made from seawater).
