I don't know if it has discharge protection, I haven't checked.
In my hds2102s (hw:1.1, fw:3.0.0) battery management is weird. When charging, the scopemeter draws about 1.9A @ 5V from the charger, which is probably about 1A/cell @ 4.2V (battery capacity 2x2600 mAh.)
After fully charging, the battery indicator drops quite quickly during operation. However, after the "battery low" message appears, the scopemeter works for another 1.5h or more. After reboot, the indicator shows a much higher battery level than before the shutdown. After a while of work, it drops again.
From what I remember in hds242 (fw: 4.1.0) the discharge indicator was better calibrated. Scopemeter worked for about 4 hours, after that time the message "battery low" appeared, and after a few minutes the device turned off.
In the photos below, 2 channels and a generator were turned on. The battery status was low, but the scopemeter was not even going to turn off.