We present calculated elastic differential cross sections for positron-acetylene scattering, obtained by using the Schwinger multichannel method. Our results are in very good agreement with quasielastic experimental data of Kauppila [Nucl. Instrum. Meth. Phys. Res. B 192, 162 (2002)]. We also discuss the existence of a virtual state (zero-energy resonance) in e(+)-C2H2 collisions, based on the behavior of the integral cross section and of the s-wave phase shift. As expected the fixed-nuclei cross section and annihilation parameter (Z(eff)) present the same energy dependence at very low impact energies. As the virtual state energy approaches zero, the magnitude of both cross section and Z(eff) are extremely enhanced (at zero impact energy). The possibility of shifting from a low-lying virtual state to a shallow bound state is not expected to significantly affect room-temperature annihilation rates.686