The effects of inter-carrier interference (ICI) and aperiodic random spreading sequences on the performance of asynchronous multicarrier code-division multiple-access (CDMA) systems with correlated fading between sub-carriers are investigated in this research. To conduct theoretical analysis for the maximal ratio combining (MRC) receiver, random parameters including asynchronous delays, correlated Rayleigh fading, and spreading sequences are averaged to find the unconditional covariance matrix of the interference-plus-noise vector. We demonstrate that the ICI in the system proposed by Kondo and Milstein (1996) can be mitigated by assigning a common random spreading sequence over all sub-carriers for each user, rather than using a set of distinct spreading sequences, where code sequences are assumed perfectly time-synchronized. Moreover, the analytic expression for the bit error probability (BEP) can be obtained with the Gaussian approximation. Simulation results are used to demonstrate the accuracy of our analysis. Various design tradeoffs including the number of sub-carriers, fading correlations, ICI and multipath effect are presented in simulation. We conclude that, when properly choosing a sufficiently large number of sub-carriers, the benefit of mitigating multipath interference and exploiting potential hidden frequency diversity shall prevail the impairment brought by increased ICI.