This paper studies the performance of quantized massive multiple-input multiple-output (MIMO) systems with superimposed pilots (SP), using linear minimum mean-square-error (LMMSE) channel estimation and maximum ratio combining (MRC) detection. In contrast to previous works, arbitrary-bit analog-to-digital converters (ADCs) are considered. We derive an accurate approximation of the uplink achievable rate considering the removal of estimated pilots. Based on the analytical expression, the optimal pilot power factor that maximizes the achievable rate is deduced and an expression for energy efficiency (EE) is given. In addition, the achievable rate and the optimal power allocation policy under some asymptotic limits are analyzed. Analysis shows that the systems with higher-resolution ADCs or larger number of base station (BS) antennas need to allocate more power to pilots. In contrast, more power needs to be allocated to data when the channel is slowly varying. Numerical results show that in the low signal-to-noise ratio (SNR) region, for 1-bit quantizers, SP outperforms time-multiplexed pilots (TP) in most cases, while for systems with higher-resolution ADCs, the SP scheme is suitable for the scenarios with comparatively small number of BS antennas and relatively long channel coherence time.