EDTA can be used on IC instruments to remove trace of contaminant cations that may "stick" to the column and alter the separation. Maybe it's not necessary in HPLC. The only few cases where I found use of EDTA in HPLC are:
Myint, K. T., Uehara, T., Aoshima, K., & Oda, Y. (2009). Polar anionic metabolome analysis by nano-LC/MS with a metal chelating agent. Analytical Chemistry, 81(18), 7766–72.
http://doi.org/10.1021/ac901269h
Pesek, J. J., Matyska, M. T., & Fischer, S. M. (2011). Improvement of peak shape in aqueous normal phase analysis of anionic metabolites. Journal of Separation Science, 34(24), 3509–16.
http://doi.org/10.1002/jssc.201100607
Asakawa, Y., Tokida, N., Ozawa, C., Ishiba, M., Tagaya, O., & Asakawa, N. (2008). Suppression effects of carbonate on the interaction between stainless steel and phosphate groups of phosphate compounds in high-performance liquid chromatography and electrospray ionization mass spectrometry. Journal of Chromatography. A, 1198-1199, 80–6.
http://doi.org/10.1016/j.chroma.2008.05.015
Köster, J., Shi, R., von Wirén, N., & Weber, G. (2011). Evaluation of different column types for the hydrophilic interaction chromatographic separation of iron-citrate and copper-histidine species from plants. Journal of Chromatography. A, 1218(30), 4934–43.
http://doi.org/10.1016/j.chroma.2011.03.036