While brand new battery would seem like a good thing, I don't know how many times you can drain a battery flat before you kill it. What I'm getting at is if your battery only a month old, draining every three days, 10 full discharges...
Yes ask the friend, at best it reduces time spent looking or at worse the lead doesn't pan out.
While it's hard to speculate, completely draining a battery in 3 days is a fair amount of power loss, if it were the GEM itself I would expect some severe damage that kept the vehicle from working. Checking the fuses yourself shouldn't be hard though, take a multimeter set to 10A current measurement range and take out a fuse at a time completing the circuit across the fuse socket contacts with the meter probes. Be careful not to touch the wrong areas, shorting whole battery current from a hot lead to ground w/o a fuse there could produce quite a spark. You might need needle tips for the probes, don't recall if the fuse boxes' contacts are exposed enough to get a normal sized meter probe tip in there or not.
I'm just not ready to assume the GEM itself needs replaced or reprogrammed. If it's shorting out I'd think the fuse would blow, or it would be physically damaged and part of the vehicle wouldn't function if it ran at all. Seems more likely the wiring to it has a fault if current leak is through that circuit, or something the GEM controls has gone haywire and disconnecting the GEM disables whatever it is. I could be wrong but IMO far too often people point at the GEM, when something else is at fault.
I'd still try unplugging the GEM to see if you can still measure significant current drain from the battery with a multimeter and while you're at it, let us know what the current drain rate is with the battery near(er) full charge level.
Also as popscat mentioned, there's the alternator. Disconnecting that should similarly show you if the battery drain stops.
