I think it can do, because group velocity can depend on frequency, so a long pulse containing low frequencies may travel at a slower speed than a short pulse containing high frequencies. this woukd be scaling the frequency of a signal, which would move it along the dispersion curve, which could change the group velocity. I don't think reducing the bandwidth of a pulse at the same frequency, to make it longer, would change its speed, though.
It s possible this might happen in a non-linear medium.
The width of the wave packet can be precisly considered with a causal solution. In frequency domain, it can not be simply evaluated. Therefore, it needs an analytical time domain solution.