As noted, the car does give you multiple warnings, from the level lines flashing (yeah, you should take note of this) right down to the turtle (this is nae, nae kiddin time).
Whilst the battery won't be "flat" in the traditional sense of no charge left, and the GOM is really only a guess of remaining range, I wouldn't like to take it into very low single digits % because you're then relying on your lowest charged cell not taking a flakey.