No, the key for the beta and the full game is different. But since they gave away free full-game/season pass keys for the PS4/XBOX1/XBOX360 on the 24hour stream I'm expecting them to do the same for the PC on the 24th.
They did say they will be doing the same for the PC release, so you can try for the full game key and maybe some other prizes then. They were also giving away season passes.