Energy detection (ED) is an attractive technique for symbol detection at receivers equipped with a large number of antennas, for example in millimeter wave communication systems. This paper investigates the performance bounds of ED with pulse amplitude modulation (PAM) in large antenna arrays under single stream transmission and fast fading assumptions. The analysis leverages information-theoretic tools and semi-numerical approach to provide bounds on the information rate, which are shown to be tight in the low and high signal-to-noise ratio (SNR) regimes, respectively. For a fixed constellation size, the impact of the number of antennas and SNR on the achievable information rate is investigated. Based on the results, heuristics are provided for the choice of the cardinality of the adaptive modulation scheme as a function of the SNR and the number of antennas.