I suppose the original M does not do this.
Because EOS M and EOS M2 firmwares are based on DSLR.
IMHO IS should be active only when shutter button is half pressed and a few seconds after(excepting touch shutter and movie rec modes).
On some lenses there is a noise when lens is powered(connected) but IS is not active(not reacting on camera movement).
But I am not sure there is a big difference in power consumption between this two modes.
It would be good if camera could measure the consumed current.