The nonlinear propagation of incoherent magnetic field-aligned electromagnetic ion-cyclotron-Alfvén (EMICA) waves in plasmas is studied. The equations governing the nonlinear interactions between incoherent EMICA waves and ion-acoustic perturbations are then used to derive a nonlinear dispersion relation, which is appropriate for investigating the modulational instability of broadband EMICA wave-packets. The case of spectral broadening of the EMICA waves is compared with the monochromatic case. It is found that the incoherency decreases the growth rate while extended regimes for the modulational instability growth rate are allowed due to the interplay between partial coherence and the dispersive effects of the EMICA waves.