IMO, of course.
I think that to the generation the 'event' happens, these people will be fighting for survival. Normalcy, where you can safely raise a family within a community (a basic human need?), will be what they are trying to ultimately achieve. This initial 'society' would be madmax-like, full of gangs and countless groups, struggling in the same way (see Jeramiah the TV show). People eeking out livings, using whatever tech savvy they had to 'fix' stuff. There really wouldn't be the infrastructure needed to 'craft' complex things. Just simple nessecities.
To the second generation, you could imagine the previous generation to have made a foothold, and made communities (safe ones) that band together to fight off the other 'bad' (controlling, fear, power-hungry) organizations. If 'safety' was established enough, communities could support someone 'who tinkered with stuff', i.e. began rediscovering, reverse-engineering, reading a book- on how to build gasoline engines, or gun powder, or some other invention. The real powerful could be using left over tech (tanks, laser guns, freeze rays?)
By the 10th generation, you could imagine that citystates have emerged, which control near-by towns, which in turn control villages or farms. So there'd be more of a medival government, but with an infrastructure. Now the towns are like late 1800s and the world has reestablished itself, only with different rules (of course ;-) There could be brewers, dancers, muscians, and well established lines of artisanship, engine makers, steel foundries, glass cutters, perhaps even like present day, without computers or something.
Anyway, my point is, I beleieve it would take generations to re-establish what we would term a society. The path being something like survial-community-infrastructure-society-nations-tiny world syndrome(instantaneous death/communication across continents).