Context. In the new era of large-scale astronomical surveys, automated methods of analysis and classification of bulk data are a fundamental tool for fast and efficient production of deliverables. This becomes ever more important as we enter the Gaia era. Aims. We investigate the potential detectability of eclipsing binaries with Gaia using a data set of all Kepler eclipsing binaries sampled with Gaia cadence and folded with the Kepler period. The performance of fitting methods is evaluated in comparison to real Kepler data parameters and a classification scheme is proposed for the potentially detectable sources based on the geometry of the light curve fits. Methods. The polynomial chain (polyfit) and two-Gaussian models are used for light curve fitting of the data set. Classification is performed with a combination of the t-distributed stochastic neighbor embedding (t-SNE) and density-based spatial clustering of applications with noise (DBSCAN) algorithms. Results. We find that ~68% of the Kepler Eclipsing Binary Catalog sources are potentially detectable by Gaia when folded with the Kepler period; we propose a classification scheme of the detectable sources based on the morphological type indicative of the light curve with subclasses that reflect the properties of the fitted model (presence and visibility of eclipses, their width, depth, etc.).