After being so dry would there be any benefits to watering with soapy water before a rain to help soil absorb the rainwater?
It couldn't hurt. I would think any kind of water would be helpful to "soften" up the ground.
I tried the soap method, I think I read it in one of Jerry Bakers books. I was more happy with just pre-wetting the soil before a rain. I could not tell if the soap helped or not, but I was unsure what the soap might have in it and what it might do to the soil. By pre-wetting with plain water ( to the point that the water would not puddle in the dust) the rain soaked in fine. I expect many soils will react differently.
I know that soap, in any concentration, will suffocate earthworms. When I was a kid, I used to dump soapy water on a likely patch of soil, and just pick up my fishing worms, as they surfaced (gasping for air).
In general, I believe it would help. The use of wetting agents makes water wetter, so to speak, so the water can be more easily absorbed by the ground. (This is why firefighters use wetting agents sometimes when fighting grass, brush or wildfires...because it affects the surface tension of the water and helps it 'stick' to whatever it hits.) If you were to do it a day or two before a good rainfall is expected, I think it would help the soil absorb more of the rainfall and would lessen the likelihood that the water would bead up and run off.
When soils exhibit hydrophobic tendencies, it usually does help if you use some form of wetting agent (many are available commercially, but homeowners often use common household-type soaps) but in a few cases, it can hurt. If you have hard water, for example, sometimes the soap can combine with certain ions in the soil and form insoluable salts and cause problems. If you don't have hard water, I wouldn't be concerned this could happen. I also don't think it would hurt, even with hard water, if this is a technique you use infrequently. It might be an issue if you have hard water and use a surfactant or wetting agent regularly.
If I were going to do it, I'd use a gentle soap like one of Dr. Bronner's castille soaps or maybe baby shampoo. I'd avoid using too high of a concentration of soap or shampoo, and I'd use only soap, not detergent. I'd avoid using anything antibacterial because it might harm the good bacteria that exists in the soil.
Your soil type and how dry it is also plays a role in how effective a wetting agent or surfactant will be.
Keep in mind that soap sprays can damage tender young plant roots and can damage the good microorganisms in your soil. Soap sprays at a high concentration of soap can be used as a herbicide or as a pesticide. I suspect you don't want to use it in those ways.
At some point this summer, folks on the GW Lawn forum were discussing core aeration of hydrophic soil and the use of soap sprays came up. Let me see if I can find and link that discussion.
Hope this helps,
Here is a link that might be useful: Lawn Forum Discussion