Yes, it sounds as though the charging system is working.
The wire in question, if it goes to the sending unit next to the alt., which is in fact the oil sending unit, would not be causing a battery drain.
The battery should be checked out and only after it has been fully charged will you get accurate test results.
Dirty or loose battery terminal connections can cause intermittent charging problems keeping a good battery from getting a good charge from the alternator.
Check the battery.
Check the connections (clean and tighten them just for piece of mind,don't go by looks alone).
Check tension on alt. belt.
Check to make sure that the crank pulley is not slipping, this can be done by chalking a line across the inner and outer parts of the balancer/crank pulley and then seeing if they still line up after it has run and been revved a few times.
If all above check out to be in good working order and the problem persists,then it is time to try to figure out what is draining the system.