The current being measured will be accurate but the voltage being supplied to the device will be affected and therefore the current measurement might not actually relate to what the device would use under normal voltage conditions, or the device might not function at all.
I am still working on my multimeter lead shootout but can say that the Digitek leads are very good buys with gold plating, nice flexible and soft insulation, nice strain reliefs on each end, and low resistance. The only two drawbacks so far are the fairly dull tips and non-silicone insulation but still very flexible.
Yes the UT136X is very small and it is a great buy but if you are going to spend another $17 on leads then the DT2843R is a much better buy with temperature, True RMS AC+DC, back light, Relative function, Min/Max function, and has great leads included already in addition to what the UT136B offers.