We study the influence of local inhomogeneities on carrier recombination dynamics in single InGaN/GaN core-shell microrods (MRs) by means of time-resolved microphotoluminescence (TRPL) at 10 K. At low carrier density (similar to 10(11) cm(-2)), the carrier recombination in the m-plane quantum well is dominated by radiative processes and the recorded decay times along the MR equally amount to about 400 ps, corresponding to a bimolecular coefficient of 1.1 +/- 0.2 x 10(-2) cm(2) s(-1). When the excited carrier density exceeds 10(12) cm(2), both the efficiency and the decay time of the PL in the quantum well drop significantly, which indicates the onset of Auger recombination. Based on a modified ABC model, we estimate a C coefficient varying from 0.5 +/- 0.2 to 2.2 +/- 0.9 x 10(-16) cm(4) s(-1) from the lower to the upper part of the MR. This increase is accompanied by a rise of PL line-width in the low excitation regime, indicating an increase of alloy disorder. Relaxation of the k-selection rule by alloy disorder is expected to play an important role in the observed increase of Auger coefficient. These results confirm that Auger recombination is sensitive to disorder and can be significantly enhanced in strongly disordered systems. We conclude that it is therefore crucial to minimize the degree of disorder in the active layer for high power LEDs based on core-shell MRs.