I do not have experienc with EDTA itself, but I have worked with DTPA (pentetic acid) and PDTA (1,3-diaminopropane-N,N,N',N'- tetraacetic acid) among other aminocarboxylate types ligands. Generally, they are not soluble at pH 7 but readily dissovle on addition of acid or base.
As Borek mentioned, soils are probably acidic or alkaline enough to cause dissociation and the EDTA will readily bind to any acceptor.