The alarm, if you have one installed, is not the immobilizer. The immobilizer is that part of every GS that won't allow the bike to start unless an authorized key is nearby. I don't know what changes to the system have been made for keyless operation.
.........I am always leaving my key in my pocket before putting on my gear!
Lord, I can't tell you HOW many hundred times I have done that and I still never learn........except it's always my truck key , since I leave the bike keys in the bike 99% of the time when it's in the trailer.