This paper considers an underlay pulsed radar-cellular spectrum sharing scenario, where the cellular system uses pilot-aided demodulation, statistical channel state information (S-CSI) estimation and limited feedback schemes. Under a realistic system model, upper and lower bounds are derived on the probability that at least a specified number of pilot signals are interfered by a radar pulse train in a finite CSI estimation window. Exact probabilities are also derived for important special cases which reveal operational regimes where the lower bound is achieved. Using these results, this paper (a) provides insights on pilot interference-minimizing schemes for accurate coherent symbol demodulation, and (b) demonstrates that pilot-aided methods fail to accurately estimate S-CSI of the pulsed radar interference channel for a wide range of radar repetition intervals.