No you cannot, because once its collecting data its initiated the discharging loads. Hooking up a charger and charging at the same time would result in the pack having a constant load. And your charger would could get damaged from the discharging load..
Good idea if only it could. IF it logged data while just being powered on that could be an option but the data logging only happens when its discharging.. Sounds like your in the market for a SPINTEC charger