This paper investigates the signal-to-interference ratios and the achievable rates of underwater acoustic (UA) OFDM systems over channels where time and frequency dispersion are high enough that (i) neither the transmitter nor the receiver can have a priori knowledge of the channel state information, and (ii) intersymbol/intercarrier interference (ISI/ICI) cannot be neglected in the information theoretic treatment. The goal of this study is to obtain a better understanding of the interplay between interference and the achievable transmission rates. Expressions for these rates take into account the ''cross-channels'' established by the ISI/ICI and are based on lower bounds on mutual information that assume independent and identically distributed input data symbols. In agreement with recent statistical analyses of experimental shallow-water data, the channel is modeled as a multivariate Rician fading process with a slowly time-varying mean and with potentially correlated scatterers, which is more general than the common wide-sense stationary uncorrelated scattering model. Numerical assessments on real UA channels with spreading factors around 10^-1 show that reliable OFDM transmissions at 2 to 4 bits/sec/Hz are achievable provided an average signal-to-noise ratio of 15 to 20 dB.