Yup, the "go to diags if connected to power" is the CRP

.
As for the charging, diags is probably designed to keep the battery in shipping range (something around 40 to 70%), so don't expect it to ever hit a green light

. On some devices, it will even discharge the battery no matter what you do.
FWIW, I just inlined dsmid's post in the CRP README, because that's where this kind of info should have been from the start (I assumed it was and completely forgot about it... :x).