yeah there is a recent beta that hit the net 2/11/2004 : DOOM III BETA 2 This version contains all patchs, the DoomConfig, DoomEditor, many new maps, a nice setup
and NVidia Drivers 41.09 for GeForce Users (to solve the problem of the grey screen)
Far as I know, Doom 3 looks to be ready within 2 months. I think I read somewhere that it'll be released near the end of April, but please bear in mind that this (as well as most other dates) are just rumours and speculation.
Your best bet would be to check out Activision's website for a definite date.
AFAIK the 'new' beta demo has been made by obsessive doom3 fans who've already started to mod (an unreleased game ) the alpha demo. I've not yet tried it as I'm content with screenies and a little alpha play
ID best hurry up though as other games developers are quickly catching up. With games such as farcry ( we all know is going to kick ass) which has official and stable playable demos, and HL2 just around the corner Doom3 has a lot to live up to.
I'm still excited as hell as I've grown up playing the countless classics released by ID.