I can't see advertising from the demand POV (which debate has been well covered) but the brand? That's another story. I think the biggest issue with Tesla and brand advertising is that if you wait until demand is an issue and your brand is in the toilet (presumably thanks to FUD) then its late and you're just hoping it isn't too late.
So, yeah, for brand perception management purposes I could see doing some advertising. If what they are currently doing (twitter, arrangements with press, etc.) is the extent of it I think it is risky to assume that it is enough. Not that I think there is anything critical about Tesla's brand identity, but I think it clearly could use some help even if it isn't strictly needed.