In order to be a "civilization" in real, historical terms, part of the implication is that cities must be involved (of course, there can be cultures without cities). If a permanent settlement exists, it always has some influence on the outside lands (in game terms, it exerts cultural pressure, since the people living there identify/pay tribute to the city, even if they're only hunter-gatherers). Therefore, even the barbarian cities have some cultural influence on the land.
In another thread in this subforum, I suggested a "tribe" mechanic, to enable a simulation of nomadic peoples - this would have no cultural borders. Ideally to me, there would also be something in-between these tribes and full-fledged cities, and that's basically what you're also suggesting. My suggestion would be to have barbarians either spawn full-fledged cities like they do currently, and also spawn some villages. The difference would be that the villages they spawn would only be capable of creating units (no buildings), would be severely limited in growth (since they're not storing food), and would have no cultural borders (and perhaps they would yield a worker and some gold if captured) - so basically a cross between a goody hut and a barbarian city.
I think this (and the tribe mechanic) would be important not just gameplay-wise, but also to add to the immersion, showing that humanity exists all over the globe whether or not they are a part of a civilization.