Cell-Free Massive MIMO systems aim to expand the coverage area of wireless networks by replacing a single high-performance Access Point (AP) with multiple small, distributed APs connected to a Central Processing Unit (CPU) through a fronthaul. Another novel wireless approach, known as the unsourced random access (URA) paradigm, enables a large number of devices to communicate concurrently on the uplink. We consider a quasi-static Rayleigh fading channel paired to a scalable cell-free system, wherein a small number of receive antennas in the distributed APs serve devices equipped with a single antenna each. The goal of the study is to extend previous URA results to more realistic channels by examining the performance of a scalable cell-free system. To achieve this goal, we construct a coding scheme that adapts the URA paradigm to various cell-free scenarios. Empirical evidence suggests that using a cell-free architecture can improve the performance of a URA system, especially when taking into account large-scale attenuation and fading.