According to the uCurrent spec sheet, the bandwidth is > 300KHz (3dB point).
It does this by having two op amps in series, with a gain of 10x each.
300KHz corresponds to a time constant of about 0.5uS... so perhaps we can say it should be possible to see a 5uS pulse at reasonable resolution with the uCurrent.
I use my uCurrent for all kinds of crazy measurements, it is surprisingly useful to have a floating battery powered x100 amp.
Try it on a signal generator and see what you get?