The effect of Cu impurities on the absorption cross section, the rate of hot exction thermalization, and on exciton recombination processes in InAs quantum dots was studied by femtosecond transient absorption. Our findings reveal dynamic spectral effects of an emergent impurity sub-band near the bottom of the conduction band. Previously hypothesized to explain static photophysical properties of this system, its presence is shown to shorten hot carrier relaxation. Partial redistribution of interband oscillator strength to sub-band levels reduces the band edge bleach per exciton progressively with the degree of doping, even though the total linear absorption cross section at the band edge remains unchanged. In contrast, no doping effects were detected on absorption cross sections high in the conduction band, as expected due to the relatively high density of sates of the undoped QDs.