I noticed this in an earlier version of NITdroid (haven't tried in a couple of weeks)
Try a neat trick:
1) connect to power
2) boot NITdroid
3) then remove battery

IIRC, NITdroid won't boot w/o a battery, but will run w/o it (Maemo doesn't).
Don't flame me if this doesn't work
Oh, and many many thanks to Solca.

EDIT:
Can't remember, but I'm almost certain NITdroid did charge the battery. When I had it in, that is