Upcoming deep imaging surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time will be confronted with challenges that come with increased depth. One of the leading systematic errors in deep surveys is the blending of objects due to higher surface density in the more crowded images; a considerable fraction of the galaxies which we hope to use for cosmology analyses will overlap each other on the observed sky. In order to investigate these challenges, we emulate blending in a mock catalog consisting of galaxies at a depth equivalent to 1.3 years of the full 10-year Rubin Observatory, a limitation imposed by the available mock data. This catalog includes effects due to weak lensing, ground-based seeing, and the uncertainties due to extraction of catalogs from imaging data. The emulated catalog indicates that approximately 12 percent of the observed galaxies are ``unrecognized'' blends that contain two or more objects but are detected as one. Using observable quantities from over half a billion galaxies, we compute shear--shear, position--position, and position--shear correlation functions after selecting tomographic samples in terms of both spectroscopic and photometric redshift bins. We examine the sensitivity of the cosmological parameter estimation to unrecognized blending employing both jackknife and analytical Gaussian covariance estimators. In both cosmic shear-only and combined clustering and weak lensing analyses, a $\sim0.025$ decrease in the derived structure growth parameter $S_8 = \sigma_8 (\Omega_{\rm m}/0.3)^{0.5}$ is seen due to unrecognized blending in both tomographies with a slight additional bias for the photo-$z$-based tomography. This decrease of $0.025$ is greater than the $2\sigma$ statistical error in measuring $S_8$. The systematic error is therefore on the same order as the statistical error. As the statistical error is expected to decrease in the future with a full 10-year dataset, the impact of the systematic error will get comparatively worse, necessitating corrections.