Humanity can likely be assumed to, under those conditions, balloon out to its former proportions (following the pattern of population increase to the point that available resources can no longer support further increase).

One possibility is that this would represent a delay in the current path and not much else, though depending on the length of time needed to rebuild our infrastructure it could make a large difference in efforts to establish humanity as safely redundant (outside Earth, that is).

Another possibility (the Oryx and Crake concept) is that due to shallow metal mining, oil depletion et cetera the current level of infrastructure would in fact not be regained, in which case the approximately-dark-ages humans would exist across the planet until it became inhabitable and they all died (even if six billion years from now).

Another (granted, comparatively unlikely) is that the various fallout from the war would prevent humanity from bouncing back in any form, in which case even the survivors would disappear relatively quickly.

One can hope that any long-term prevention for the overpopulation consequences that might have been used in that future could also be used in our future. (Personally, hoping for the Singularity approach, which seems much harder to achieve without an Internet and with a much smaller population slowly spreading out and starting to rebuild the ruins of empire.)