The realistic simulation of variable star populations is fundamental to determine the selection function and contamination in existing and upcoming multi-epoch surveys. We present ELLISA, a simulator that produces an ensemble of mock light curves for a population of eclipsing binaries obtained from physical and orbital parameters consistent with different Galactic populations, and which considers user-supplied time sampling and photometric errors to represent any given survey. We carried out a search for eclipsing binaries in the QUEST low Galactic latitude catalogue of variable stars, spanning an area of 476 deg(2) at -25 degrees less than or similar to b less than or similar to 30 degrees and 190 degrees <= l <= 230 degrees towards the Galactic anticentre, and use ELLISA to characterize the completeness of the resulting catalogue in terms of amplitudes and periods of variation as well as eclipsing binary type. The resulting catalogue consists of 1125 eclipsing binaries, out of which 179, 60, and 886 are EA, EB, and EW types, respectively. We estimate, on average, 30 per cent completeness in the period range 0.25 less than or similar to P/d less than or similar to 1 for EB-FEW binaries and 15 per cent completeness for EA binaries with periods 2 less than or similar to P/d less than or similar to 10, being the time sampling the primary factor determining the completeness of each type of eclipsing binary. This is one of few eclipsing binary catalogues reported with an estimate of the selection function. Mock eclipsing binary light-curve libraries produced with ELLISA can be used to estimate the selection function and optimize eclipsing binary searches in upcoming multi-epoch surveys such as Gaia, the Panoramic Survey Telescope and Rapid Response System, the Zwicky Transient Factory, or the Large Synoptic Survey Telescope.