Continuous aperture arrays (CAPAs) have emerged as a promising physical-layer paradigm for sixth generation (6G) systems, offering spatial degrees of freedom beyond those of conventional discrete antenna arrays. This paper investigates the interaction between the CAPA receive architecture and low-cost 1-bit analog-to-digital converters (ADCs), which impose a severe nonlinear distortion penalty in conventional discrete systems. For Rayleigh fading, we derive a moment matching approximation (MMA)-based closed-form symbol error probability (SEP) approximation based on Gamma moment-matching of the spatial eigenvalue distribution, and show that CAPAs incur a diversity-order penalty governed by Jensen's inequality on the mode eigenvalues. For line-of-sight (LoS) propagation, we prove that CAPA achieves exactly the unquantized additive white Gaussian noise (AWGN) performance bound under perfect spatial and phase alignment, completely eliminating the 1-bit penalty that forces discrete systems to double their antenna count. Monte Carlo simulations under Rayleigh, Rician, and LoS conditions validate all analytical results.