Increased bandwidth in future communications systems could lead to disproportionately increased power consumption of the analog-to-digital converter (ADC). To avoid this, a promising solution is the employment of temporally oversampled 1-bit quantization at the receiver, which drastically reduces ADC circuit complexity and, thus, promises reduced power consumption. However, the resulting non-linearity requires the redesign of receiver synchronization algorithms. In this paper, we focus on the influence of timing offsets in the receive signal on the system performance in terms of the mutual information rate between transmitter and receiver, considering zero-crossing modulation (ZXM). We show the principal limits of timing synchronization in the digital domain and investigate the suitability of a well-known polynomial filter based timing synchronization algorithm for the use with 1-bit quantization. Our results demonstrate its suitability and, thus, provide an important step towards the practical realization of receivers with temporally oversampled 1-bit quantization.