In this paper, we investigate the impact of correlation between the energy and information links in wireless power transfer systems, from a physical layer security perspective. With that aim, we first determine how correlation can affect system capacity in practical energy harvesting set-ups in the absence of eavesdroppers. We quantify that even though link correlation improves the average signal-to-noise ratio (SNR) for a fixed transmit power, it also increases its variance, which ultimately degrades capacity. Based on this observation, we show that correlation between the energy and information links may be detrimental/beneficial for the secrecy capacity in the high/low legitimate SNR regime, whenever such correlation affects the legitimate user. Conversely, we also point out that when link correlation for the wiretap link is rigorously accounted for, it barely affects secrecy performance, causing only a minor degradation in some instances.