If the pixels were literally black that would be the case, but even on very underexposed pictures I don't think that ever happens. There's still photons on the sensor, it's just that they are swamped by the noise. Like, most DSLRs nowadays capture 12-bit values, which suggests you would have to underexpose by something on the order of 12EV to truncate the output to zero.
Yes, and that is very, very possible. In any case, doing that would give you some relatively painful quantisation error, which is why the HDR approach works better.