Yes.
I made up the salt water solutions the day before, and stirred them occasionally.
I wasn't so worried about precisely how much salt was in the final solution as long as it was saturated at the ambient temperature (winter soap would have less salt this way, but I don't mind).
Just before I strained the salt water into fresh containers (to add the lye into) they did have salt both at the bottom and in flakes around the rim.
The salt water was clear after straining.
When I added the lye to the salt water, I stirred it and then left it to dissolve. When it cooled, some of the salt was out of solution and had formed a sediment of minature crystals on the bottom, and there were just a few very thin flat crystals on the surface that broke up on stirring. The solution became smoothly cloudy (and stayed cloudy, although some sediment would settle again) when I stirred.
There aren't any large crystals of salt in the final soap, so the soleseife soap is very smooth.