Gravity is a small force on ions when compared to water flow and diffusion; lead ions won't sink in a graduated cylinder. But rather than ponder the drift upwards of ions from the concrete, consider the drift downwards of ions from the soil. For instance, the soil may be acidic, and will almost always have more water in it than the concrete has, so the acids in the soil will be much more mobile than the ions in the concrete, and will fairly easily drift into the concrete, neutralizing $\ce{Ca(OH)2}$ or even dissolving $\ce{CaCO3}$. Whether these calcium ions will travel upwards... well, yes, but calcium compounds may adsorb on soil particles and travel even slower. So the soil may be as much a barrier as the concrete is a poor source of ions.
Concrete may lose some ions (especially $\ce{Ca(OH)2}$) in contact with flowing water, but even more, it tends to pick up $\ce{CO2}$ and the $\ce{Ca(OH)2}$ becomes $\ce{CaCO3}$, which is less soluble. So the soil right next to the concrete may be a little more alkaline than the soil at the top surface.
