The searching for StEllar Counterparts of COmpact high velocity clouds (SECCO) survey is devoted to the search for stellar counterparts within ultra compact high velocity clouds that are candidate low-mass, low-luminosity galaxies. We present the results of a set of simulations aimed at the quantitative estimate of the sensitivity of the survey as a function of the total luminosity, size, and distance of the stellar systems we are looking for. For all of our synthetic galaxies we assumed an exponential surface brightness profile and an old and metal-poor population. The synthetic galaxies are simulated both on the images and on the photometric catalogues, taking all the observational effects into account. In the fields where the available observational material is of top quality (≃36% of the SECCO fields), we detect synthetic galaxies as ≥5σ over-densities of resolved stars down to μV,h ≃ 30.0 mag/arcsec2, for D ≤ 1.5 Mpc, and down to μV,h ≃ 29.5 mag/arcsec2, for D ≤ 2.5 Mpc. In the field with the worst observational material of the whole survey, we detect synthetic galaxies with μV,h ≤ 28.8 mag/arcsec2 out to D ≤ 1.0 Mpc, and those with μV,h ≤ 27.5 mag/arcsec2 out to D ≤ 2.5 Mpc. Dwarf galaxies with MV = -10.0, with sizes in the range spanned by known dwarfs, are detected by visual inspection of the images up to D = 5 Mpc independent of the image quality. In the best quality images, dwarfs are partially resolved into stars up to D = 3.0 Mpc and completely unresolved at D = 5 Mpc. As an independent test of the sensitivity of our images to low surface brightness galaxies, we report on the detection of several dwarf spheroidal galaxies probably located in the Virgo cluster with MV ≲ -8.0 and μV,h ≲ 26.8 mag/arcsec2. The nature of the previously discovered SECCO 1 stellar system, also likely located in the Virgo cluster, is rediscussed in comparison with these dwarfs. While specific for the SECCO survey, our study may also provide general guidelines for the detection of faint stellar systems with 8 m class telescopes. Based on data acquired using the Large Binocular Telescope (LBT). The LBT is an international collaboration among institutions in the United States, Italy, and Germany. The LBT Corporation partners are The University of Arizona on behalf of the Arizona university system; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, the Astrophysical Institute Potsdam, and Heidelberg University; The Ohio State University; and The Research Corporation, on behalf of The University of Notre Dame, University of Minnesota, and University of Virginia.