There would be no factions.
Does there really need to be? Im sure some factions could be created though. Just not
countries like the NCR. Groups of people who share a common goal however (I'm sure) could be thought up for this setting.
So again, no real factions and no mutations which means would not make a good Fallout game/RPG.
Prehaps the horrors of the beginings of mutations could be part of the storyline however. It also doesn't necessarily have to be a "run and gun," the setting could involve things like choosing whether or not to help your fellow survivors and maintain that shed of decent humanity that existed before the war.
Maybe it wouldn't be a "true" Fallout game, but then, there seems to be alot of debate on these forums as to just what the definition of a "true" fallout game entails. For me, its a game which is able to give a brilliant and atmostpheric setting of a post-nuclear holocaust world (not necessarily realistically though, ie. mutations), and a game set just after the war could achieve that brilliantly.