YES! And in a lot more ways than you might appreciate.
First and foremost, I wouldn't discount the "occasional dead leaves or branches". Those leaves and branches break down, feeding bacteria and fungus in the soil, as well as leaving organic matter that helps hold moisture and improve nutrient availability. The roots go deep, and will bring up minerals that aren't necessarily available in the upper levels of soil. When leaves and branches are left in place, the minerals accumulated in them will then be present in the higher levels of the soil.
Second, roots actually exude organic compounds.
These exudates feed bacteria in the soil, suppress harmful pathogens, and do a lot of other cool stuff.
Third, plants prevent erosion from wind and rain. This doesn't necessarily directly improve soil, but it does definitely slow down how fast organic material and other good stuff is removed from the soil in the area.
Finally, some plants (legumes being the classic example) are capable of forming a symbiotic relationship with bacteria in the soil, and actually pull nitrogen out of the atmosphere fixing it in the soil (sort of, it ends up in nodules on the roots usually. When the plant dies, the nodules break down releasing nitrogen)