Your theory is correct - until the earthworms and other soil-living critters eat it. However, if you have a cheap source (cheaper than free leaves), by all means, go for it.

FWIW, I have root knot nematodes & I was told by a county extension person that it's better not to disturb the soil too much - better to pile the organic matter on top and just lightly mix the first couple of inches, if you must. Macroorganisms will mix it in for you anyway.

For me, it works better at moisture retention, since the sand just seems to swallow up any organic matter I mix in deeply.

Indeed - and they have FAQs.

Carol, that's what I do. I just toss everything on top and let nature do its job. Nature doesn't dig organic matter into the soil, because earthworms and other critters come out at night and do their work. That's why "the early bird catches the worm," because the worms are still on the top of the soil eating in the very early morning. People think I'm crazy to do that until they see my beautiful rich soil. It does take longer this way, around three years or so to get really good soil, but it worked on the nasty marl soil at my old house, and it works on the horrid sandy soil here.

I went to the zoo and got their free compose. Thought it would disappear into the sand. But as you say it took about 3 seasons to get good, rich soil that stayed.