In my research I found that the majority of the bacteria forms on a solid surface - I thought that was the whole Idea of biological filtration and a big part of why current is so important - it circulates the water over the bacteria colony, feeding it nitrites etc... I'm not sure what you think live rock does if it isn't a host for bacterial colonies.
However, I do know of an old fish keeper who runs a shop in Little Tokyo, who keeps small salt-water tanks healthy with nothing but an airstone, so what you are saying is possible. Still I think even in that case most of the bacteria is in the sand. That guys is something of a magician though, I don't know how he does it...
If bacteria were able to maintain a population in open water, what's the point of bioligcal filters and sumps that run water through sponges, ceramic rings, live rock etc?