The recent works on a deep learning (DL)-based joint design of preamble set for the transmitters and data-aided active user detection (AUD) in the receiver has demonstrated a significant performance improvement for grant-free sparse code multiple access (GF-SCMA) system. The autoencoder for the joint design can be trained only in a given environment, but in an actual situation where the operating environment is constantly changing, it is difficult to optimize the preamble set for every possible environment. Therefore, a conventional, yet general approach may implement the data-aided AUD while relying on the preamble set that is designed independently rather than the joint design. In this paper, the activity detection error rate (ADER) performance of the data-aided AUD subject to the two preamble designs, i.e., independently designed preamble and jointly designed preamble, were directly compared. Fortunately, it was found that the performance loss in the data-aided AUD induced by the independent preamble design is limited to only 1dB. Furthermore, such performance characteristics of jointly designed preamble set is interpreted through average cross-correlation among the preambles associated with the same codebook (CB) (average intra-CB cross-correlation) and average cross-correlation among preambles associated with the different CBs (average inter-CB cross-correlation).