Farmerjohn:
In answer to your question: it depends. Here are some things to take into consideration.
1. Alkaline soil has a tendency to form caliche (hardpan) just a few inches below the topsoil. Caliche is really calcium carbonate. If you do have caliche, and it's close to the surface (within two to three inches) then the water will simply hit the caliche and drain out, especially if there is a slope, or it will simply evaporate. At that point, it won't matter what the pH of the water is, since it won't stay in the ground, it will be pointless. It could also cause serious erosion.
2. Do you have anything growing on your land? Is there grass, or something type of cover crop there that could help trap the water?
3.The slower you can trickle the water, the more likely it will be absorbed. If you plant to use a pump, and gush the water out onto your land, then you're just going help build more caliche closer to the surface, and will get very little benefit from the water.
4. If you don't have anything growing on the land, and want to lower the pH, till in 1.2 oz. of ground rock sulfur per square yard into the soil. But if you have few microbes or macro-organisms in your soil, till in sawdust, composted leaves, wood chips, cottonseed meal or leaf mold into the soil. This will encourage micro- and macro-organisms to grow quickly in the soil. Then I would create linear ditches perpendicular to any slope, about three feet apart, mounding the dirt between the ditches. I would then put the water into the ditches, letting it soak the mounded soil.
It might take a little longer, but you can really improve the soil (lower pH and increase microbial and invertebrate actions in the soil) significantly. I don't usually recommend tilling, because it tends to bring undesireable seeds closer to the surface, and forces germination (some seeds can remain viable than a century in desert soils).
E-mail me back in this column as to whether you have anything growing on your land, if you have caliche, and if your land has a slope, and I'll try to assist you in getting your pool emptied and used on your land.

Here is a link that might be useful: Desert Gardens