The authentication of wireless devices through physical layer attributes has attracted a fair amount of attention recently. Recent work in this area has examined various features extracted from the wireless signal to either identify a uniqueness in the channel between the transmitter-receiver pair or more robustly identify certain transmitter behaviors unique to certain devices originating from imperfect hardware manufacturing processes. In particular, the carrier frequency offset (CFO), induced due to the local oscillator mismatch between the transmitter and receiver pair, has exhibited good detection capabilities in stationary and low-mobility transmission scenarios. It is still unclear, however, how the CFO detection capability would hold up in more dynamic time-varying channels where there is a higher mobility. This paper experimentally demonstrates the identification accuracy of CFO for wireless devices in time-varying channels. To this end, a software-defined radio (SDR) testbed is deployed to collect CFO values in real environments, where real transmission and reception are conducted in a vehicular setup. The collected CFO values are used to train machine-learning (ML) classifiers to be used for device identification. While CFO exhibits good detection performance (97% accuracy) for low-mobility scenarios, it is found that higher mobility (35 miles/h) degrades (72% accuracy) the effectiveness of CFO in distinguishing between legitimate and non-legitimate transmitters. This is due to the impact of the time-varying channel on the quality of the exchanged pilot signals used for CFO detection at the receivers.