As of right now there is still no word on progress, and if it will transfer or not (other than the fact you can unlock some Beta exclusive content for the final game), but hopefully we will learn more on this matter soon. While the Alpha progress didn't transfer, it was only two short missions long, with a single open area for side quests, and a single mode competitive mode. Meanwhile, the Beta version actually has a pretty good chunk of the main game, and Bungie also stated that they would be treating this beta as a "full release" back when the game was first announced. While this doesn't mean progress will transfer, it does give us hope. Still, even if it doesn't, don't let it stop you from checking this one out. If you don't want to spoil the full game, at least check it out for the Beta exclusive unlockables. You won't be sorry.
[UPDATE] The Beta is out, and it includes over 6 missions, but only two multiplayer maps.