I may not be reading all the specs correctly ( https://cdn.sparkfun.com/datasheets/Too ... alRev1.pdf
) but it looks like it MIGHT be able to indirectly measure current down in that range with the type of set up they used in the video (ground cable as external shunt). They claim a noise floor "as low as 1 microvolt." The manual suggests accuracy of +/- (0.5% + 0.5 microvolt) in the lowest range. IIRC, for their demonstration they had an estimated 3 milliOhm resistance ground cable, which suggests 1 mA could be measured with reasonable accuracy (subject to error in resistance estimate):
3uV/3milliOhm=1mA ; 3uV*0.005 + 0.5uV=0.515uV ...assuming I didn't misinterpret the tables...
I suppose you could also increase sensitivity/accuracy quite a bit by temporarily replacing the ground cable with smaller gauge wire of known resistance. I imagine that would be OK as long as the car stays off.
It looks like data logging can be started and stopped via the app and the log files are named with a time/date stamp (presumably when log starts?) so I guess you could figure out time of day etc from that plus interval X # of data points.