Integrated Sensing and Communication (ISAC) systems enable cellular networks to jointly operate as communication technology and sense the environment. While opportunities and potential performance have been largely investigated in simulations, few experimental works have showcased Automatic Target Recognition (ATR) effectiveness in a real-world deployment based on cellular radio units. To bridge this gap, this paper presents an initial study investigating the feasibility of ATR for ISAC. Our ATR solution uses a Deep Learning (DL)-based detector to infer the target class directly from the radar images generated by the ISAC system. The DL detector is evaluated with experimental data from a ISAC testbed based on commercially available mmWave radio units in the ARENA 2036 industrial research campus located in Stuttgart, Germany. Experimental results demonstrate accurate classification performance, demonstrating the feasibility of ATR ISAC with cellular hardware in our setup. We finally provide insights about the open generalization challenges, that will fuel future work on the topic.