alarm has its own backup battery but it will NOT last more than a few moments... once the battery disconnected, manually or via the battery disconnect device, there will be no electrical functions in the car, no alarm, nothing...

I do electronics for living and one of the troubleshotting processes is to start from the very basic begining and move on to the next complex point without skipping a step...

disconnecting a (-) battery terminal overnight will cost you one day's worth of time, and if the battery is good, as they suggested, all you lost, is a night...

if the battery is not good (a bad batch from the manufacturer), and you have gone through all the tests, and eventually came back to the battery, that would be very upsetting...

as far as fuses - you need to write down on a piece of a paper which fuses you are going to take out, and which ones you are putting back in - documenting this process will save you alot of headaches in the future... alarm is the item that stays on even after the car is gone to sleep... you will want to have alarm turned off at some step during testing... if you have access to the WDS diagram, look at the supply fuses to various modules, and have them removed... cross reference each fuse that you are pulling to make sure you are not disabling something without your explicit knowledge...

chasing this kind of a gremlin is no fun...