This study addresses the scientific question of the applicability of low-cost antennas to the most precise GNSS applications. First of all, we inspect the implications of the availability and quality of low-cost antenna PCC models for precise positioning. From this point of view, we analyze the selected performance indicators of multi-constellation positioning with the representative set of low-cost mass-market GNSS receiver antennas. The processing strategy was based on the relative positioning model, considered the most reliable and precise one. To isolate the antenna-related errors from atmospheric propagation ones, we conducted an experiment based on an ultra-short baseline. As the main indications of low-cost antenna performance, we considered distance and height residuals, defined as the difference between benchmarks and the retrieved from GNSS measurements. We found that the low-cost antenna's PCV effect may significantly affect the final results. On the other hand, the results obtained using certain configurations of low-cost antennas were characterized by only slightly higher standard deviations and discrepancies with respect to benchmark values than those obtained with surveying or geodetic equipment. We identify several sets of low-cost antennas where distance residuals do not exceed 4 mm and height residuals do not exceed 6 mm, which shows the low-cost antenna performance comparable to those achieved using high-grade antennas. On this basis, we conclude that selected low-cost antennas can meet the requirements of high-precision surveying applications.