The absolute current value probably doesn't matter - in fact I very much doubt a hobbyist-level multimeter is even capable of accurately measuring the (fractions of?) millivolts across a fuse.

It's more important as a boolean signal - "is there current being drawn on this fuse?", and then usually even those fractions of millivolts will generally be enough to make your el-cheapo multimeter register 1mV and tell you something is drawing current, where as a fuse with no voltage drop across it at all will reliably show 0mV (just like it would if the probes were shorted) on even a cheap meter.