Stephen Hawking was thinking about the universe (as we know it) as a "bubble", outside which "anything" would be "nothing" to us because it doesn't exist in our space and therefore we couldn't ever be aware of it. However, that wouldn't be "nothingness", but it's an interesting question.
Anyway, I think the answer is YES, nothingness can exist.
I dont' think distance is essential. It is not difficult to describe something in a system with one, two or three dimensions, or even none: an infinitely small point.
The key thing would be, that if TIME doesn't exist in a space, then there would be nothingness.
TIME is required to define or describe anything we know - particles, energies, forces, light, magnetic field, etc.
But if time wouldn't exist in that space - none of those would exist, either.
The way I understand Hawkings "bubble" is, that the reason why we couldn't understand anything outside this our bubble is because the time-space is bent so that we cannot travel outside, nor observe anything beyond that.
But if time and time-space is so heavily bent, that it forms a shell around our bubble, and the space outside lacks a time-dimension - then nothing would exist, resulting in complete nothingness.