We present an evaluation of systematic effects associated with a continuously rotating, ambient-temperature half-wave plate (HWP) based on two seasons of data from the Atacama B-Mode Search (ABS) experiment located in the Atacama Desert of Chile. The ABS experiment is a microwave telescope sensitive at 145 GHz. Here we present our in-field evaluation of celestial (Cosmic Microwave Background (CMB) plus galactic foreground) temperature-to-polarization leakage. We decompose the leakage into scalar, dipole, and quadrupole leakage terms. We report a scalar leakage of ∼0.01%, consistent with model expectations and an order of magnitude smaller than other CMB experiments have been reported. No significant dipole or quadrupole terms are detected; we constrain each to be <0.07% (95% confidence), limited by statistical uncertainty in our measurement. Dipole and quadrupole leakage at this level lead to systematic error on r ≲ 0.01 before any mitigation due to scan cross-linking or boresight rotation. The measured scalar leakage and the theoretical level of dipole and quadrupole leakage produce systematic error of r < 0.001 for the ABS survey and focal-plane layout before any data correction such as so-called deprojection. This demonstrates that ABS achieves significant beam systematic error mitigation from its HWP and shows the promise of continuously rotating HWPs for future experiments.