The wiretap channel is a well-studied problem in the physical layer security literature. Although it is proven that the decoding error probability and information leakage can be made arbitrarily small in the asymptotic regime, further research on finite-blocklength codes is required on the path towards practical, secure communication systems. This work provides the first experimental characterization of a deep learning-based, finite-blocklength code construction for multi-tap fading wiretap channels without channel state information. In addition to the evaluation of the average probability of error and information leakage, we examine the designed codes in the presence of fading in terms of the equivocation rate and illustrate the influence of (i) the number of fading taps, (ii) differing variances of the fading coefficients, and (iii) the seed selection for the hash function-based security layer.