According to Bethesda, not only will progression be carried over from the beta, but the beta release will essentially be the full game itself. This means that unlike some betas which only allow players to experience parts of the game, the Fallout 76 beta will be the entire game which means that players will be able to enjoy the game in its entirety, explore every nook and cranny, and so on.
However given that this is a beta, as Bethesda notes, things could change ahead of the final release so what you see might not necessarily be what you expect. That being said, it should be noted that the Fallout 76 beta is not an open beta. This means that not everyone will get to participate in it. Instead players who do wish to check out the beta can do so by pre-purchasing the game, otherwise gamers will just have to wait until the game is release which is currently set for November.