Bandwidth overages currently aren’t billed or counted (source), so nothing will happen. But that’s basically abuse of the system and they could change that at any time (although not without telling you first)… if that ever happened you would have to upgrade your Droplet to one that fits your needs, pretty simple.

For some reason, you can’t check your bandwidth usage in the control panel, but they would definitely add that functionality if they ever were to start billing for it. So no need to worry about it at all.