Simultaneous wireless information and power transfer can be realized by means of an integrated receiver, where both the energy harvester and the information decoder operate on the rectified received signal. We investigate the effect of the non-linearity of the rectifier on the error performance of the information decoder when transmitting over a Nakagami-m fading channel. Through analysis and simulation, we demonstrate that the low-noise error performance strongly depends on the small-signal behavior of the rectifier, even when the average operating point is outside the small-signal area. Approximating for analysis purposes the rectifier by a quadratic detector yields accurate bit error rate results for the fading channel in the low-noise regime, whereas an over-optimistic error performance is obtained when applying the envelope detector approximation.