Wi-Fi systems based on the IEEE 802.11 standards are the most popular wireless interfaces that use Listen Before Talk (LBT) method for channel access. The distinctive feature of a majority of LBT-based systems is that the transmitters use preambles that precede the data to allow the receivers to perform packet detection and carrier frequency offset (CFO) estimation. Preambles usually contain repetitions of training symbols with good correlation properties, while conventional digital receivers apply correlation-based methods for both packet detection and CFO estimation. However, in recent years, data-based machine learning methods are disrupting physical layer research. Promising results have been presented, in particular, in the domain of deep learning (DL)-based channel estimation. In this paper, we present a performance and complexity analysis of packet detection and CFO estimation using both the conventional and the DL-based approaches. The goal of the study is to investigate under which conditions the performance of the DL-based methods approach or even surpass the conventional methods, but also, under which conditions their performance is inferior. Focusing on the emerging IEEE 802.11ah standard, our investigation uses both the standard-based simulated environment, and a real-world testbed based on Software Defined Radios.